Abstract:
A system for maintaining routing tables at each router in a computer network. The system is based on (a) a feasibility condition that provides multiple loop-free paths through a computer network and that minimizes the amount of synchronization among routers necessary for the correct operation of a routing algorithm, and (b) a method that manages the set of successors during the time it synchronizes its routing-table update activity with other routers, in order to efficiently compute multiple loop-free paths, including the shortest path, through a computer network.

Description:
FIELD OF THE INVENTION 
     The present invention relates to processes and devices used to route data packets from an end station (host computer) to another end station. The end stations may be in different computer networks. 
     BACKGROUND OF THE INVENTION 
     In a computer network or internetwork, there is a problem of physically routing message traffic (data packets) between nodes and providing the shortest path between any two nodes. A computer network is formed of three or more nodes connected by links. Each node may be a general-purpose computer or a specialized device, such as a router or switch. A link is a communication path that connects two or more nodes with one another. An internetwork is formed of multiple computer networks interconnected by nodes, each node may be a general-purpose computer or a specialized device, such as a router. Each link has a length (or cost) associated with it. A bidirectional link has a length in each of its two directions. A broadcast link has a single cost. A network path also has a single length or cost associated with it. Once a shortest path is provided, the number of nodes or the length of a link in the network may change so that a new shortest path must be found. Because providing a shortest path uses computer resources, and because routing traffic inefficiently wastes network resources, it is important to quickly and accurately find each shortest path. 
     Data packets may, for example, be routed from an end station in one network to an end station in another network. The devices that route the data packets (routers) map the address of a destination network or end station into either a path or the next router (or successor) along the path to the destination. To accomplish their function, routers need to implement a routing protocol, which supports two main functions: route computation and data packet forwarding. 
     Three types of approaches exist in the prior art for providing a shortest path. The first type is the link-state approach (also called a topology-broadcast approach), wherein a node must know the entire network topology. Each router uses this information to compute the shortest path and successor router (or next hop) in the path to each destination. The node broadcasts update messages to every node in the network or internetwork. Each node originates update messages containing the cost of the links adjacent to that node and forwards updates received from other nodes, taking care to ensure that the same update is not forwarded more than once. Well known examples of the link-state approach are the new ARPANET routing protocol and the OSPF (Open Shortest Path First) protocol. A primary disadvantage of the link-state approach is that the maintenance of an up-to-date version of the entire network topology at every node may constitute excessive storage and communication overhead in a large network. Another disadvantage is that the path computations required by the link-state approach are computationally expensive. A third disadvantage is that the shortest perceived path may contain loops, which lengthen a path and cause data packers to visit the same node multiple times. The existence of loops, even temporarily, is a detriment to overall performance of a computer network. 
     The distance-vector approach requires that a router knows only the distances to its own destinations and to those destinations reported by other nodes, together with some additional information that varies depending on the particular protocol. The router maintains the length of the shortest path from each of its adjacent nodes to every destination node and the next node in that shortest path. The node sends update message, containing (as a minimum) distance to other nodes, to only its adjacent nodes. Well known examples of the distance vector approaches are RIP (Routing Information Protocol), RIPv2 (RIP version 2), BGP (Border Gateway Routing Protocol), and Cisco&#39;s proprietary EIGRP (Enhanced Interior Gateway Routing Protocol). 
     RIP and RIPv2 use variants of the distributed Bellman-Ford (DBF) algorithm for shortest-path computation. The main disadvantages of protocols based on DBF are the creation of routing loops and the possibility of counting to infinity. A node counts to infinity when it increments its distance to a destination node, until a predefined maximum value is reached. A number of attempts have been made to solve the counting to infinity and looping problems by increasing the amount of information exchanged among nodes or by making nodes disregard link changes for a predefined period of time before updating their routing tables. None of these approaches, however, has been successful. 
     BGP includes the complete path to a destination in a routing-table update. Because nodes can determine if they are part of a path reported by a neighbor node to a destination, they avoid long-term loops and counting to infinity. 
     A patent illustrative of the distance vector approach is U.S. Pat. No. 4,466,060 to Riddle. The Riddle patent disclosed an adaptive distributed message routing algorithm where each node transmits different information to its adjacent nodes. The transmitted routing information arranges the nodes of the network in a hierarchical fashion that takes on the graphical form of a tree structure with the transmitting node at the root of the tree and the remaining nodes stemming from the root. A similar approach to the Riddle patent is used by Garcia-Luna-Aceves and Murthy in &#34;path finding algorithms&#34; (J. J. Garcia-Luna-Aceves and S. Murthy, &#34;A Path-Finding Algorithm for Loop-Free Routing,&#34; IEEE/ACM Transactions on Networking, February 1997) as well as others (e.g., P. Humblet, &#34;Another Adaptive Shortest-Path Algorithm&#34;, IEEE Transactions on Communications, Vol.39, No.6, June 1991, pp. 995-1003; B. Rajagopalan and M. Faiman, &#34;A Responsive Distributed Shortest-Path Routing Algorithm within Autonomous Systems,&#34; Internetworking: Research and Experience, Vol.2, No.1, March 1991, pp. 51-69). In this type of distance-vector algorithms, a node communicates to its neighbors its shortest path routing tree by incrementally sending the distance and second-to-last hop node identifier to each destination. These algorithms eliminate counting to infinity, and the loop-free path finding algorithm by Garcia-Luna-Aceves and Murthy eliminates routing loops as well. 
     EIGRP eliminates counting to infinity and looping using the Diffusing Update Algorithm (DUAL) (J. J. Garcia-Luna-Aceves, &#34;Loop-Free Routing Using Diffusing Computations,&#34; IEEE/ACM Transactions on Networking, Vol. 1, No. 1, February 1993). DUAL selects routes to be inserted into a routing table based on feasible successors. A successor is a neighboring router used for packet forwarding that has a least-cost path to a destination that is guaranteed not to be part of a routing loop. From router i&#39;s standpoint, a feasible successor toward destination j is a neighbor router k that satisfies a feasibility condition that is based on values such as the router&#39;s own distance and its neighbor&#39;s distance to the destination. 
     The three feasibility conditions in the prior art are the DIC (Distance Increase Condition) and the CSC (Current Successor Condition) and the SNC (Source Node Condition). The DIC can be summarized as follows: If a node i detects a decrease in either 
     1. the length of a link to one of its adjacent neighbors or 
     2. the distance from an adjacent node to a destination node 
     then node i can choose any adjacent neighbor as the new successor node en route to the destination node, provided that the sum of the length from node i to the adjacent neighbor and the length from the adjacent neighbor to the destination node is less than or equal to the smallest assigned length from node i to the destination node. 
     The CSC can be summarized as: If a node i detects a change in either 
     1. the length of a link to one of its adjacent neighbors or 
     2. the distance from an adjacent node to a destination node 
     then node i can choose any adjacent neighbor as the new successor node en route to the destination node, provided that the length from the new adjacent neighbor to the destination node is less than or equal to the smallest assigned length from the original adjacent neighbor to the destination node. 
     The SNC can be summarized as: If a node i detects a change in either 
     1. the length of a link to one of its adjacent neighbors or 
     2. the distance from an adjacent node to a destination node 
     then node i can chose any new adjacent neighbor as long as the length from the adjacent neighbor to the destination node is less than the feasible distance from node i to the destination. The feasible distance is the minimum of all of the distances to the destination that node i has reported since the last time node i either initialized itself or began its participation in a diffusing computation. 
     When the feasibility condition is met, node i can carry out a local computation to determine a new path independently of other nodes, thus saving computational resources. It is important to realize, however, that the feasibility conditions DIC, CSC, and SNC are not always met. When a feasibility condition is not met at a node i, node i must perform a diffusing computation, wherein node i must coordinate with other nodes to find a new shortest path. The SNC can be met easier than the DIC or CSC, for example, and thus the SNC allows for fewer diffusing computations than these other feasibility conditions. Therefore, because it is important to meet a feasibility condition as often as possible to save computational resources, there has been a need to develop feasibility conditions that can be more easily satisfied in order to avoid diffusing computations as much as possible. 
     As mentioned above, diffusing computations require larger amounts of computer resources than local computations. One prior art system supports multiple diffusing computations concurrently by maintaining bit vectors at each node. The bit vectors specify, for each adjacent node and for each destination node, the number of correspondences which were originated by and the number of correspondences which must be answered by the node maintaining the bit vector. The problem with this system is that the bit vectors can become exceedingly large in a large network, thus consuming large amounts of computational resources. Another prior art system eliminates these bit vectors by requiring a node to `freeze` a designated successor as long as the node is part of the diffusing computation (i.e., while a diffusing computation proceeds for a particular destination, each node participating in the diffusing computation for that destination must keep the same next hop for that destination). In addition, a node is only allowed to participate in one diffusing computation at a time for each destination. A state machine is used to process messages that arrive at a node while the node participates in a diffusing computation, and determines if a new diffusing computation is necessary after the previous one terminates. This prior art system classifies routing messages as updates, queries, and replies. Queries and replies are used for coordinating diffusing computations. In all of the prior art systems based on diffusing computations and feasibility conditions, the feasibility conditions are based on the current value of link costs and of distances reported by neighbors, and a node raises its feasible distance only when it starts or joins a diffusing computation. 
     Thus, even though diffusing computations of the prior art may provide correct results, they are inefficient. Because of this inefficiency, there has been a need in the prior art to develop new approaches to diffusing computations which are able to conserve computational and communication resources. In addition, while prior art systems based on feasibility conditions can provide multipath routing in the absence of diffusing computations, these systems can provide only a single successor during the course of a diffusing computation, and must wait until the diffusing computation terminates before providing a better path. The result of this constraint is that even if a better path to the destination is becomes available, that path cannot be used until the diffusing computation terminates. 
     The third approach to routing in computer networks and internetworks is the approach based on link vector algorithms (J. J. Garcia-Luna-Aceves and J. Behrens, &#34;Distributed, Scalable Routing based on Vectors of Link States,&#34; IEEE Journal on Selected Areas in Communications, Vol 13, No. 8, October 1995). The basic idea of LVA consists of asking each node to report to its neighbors the characteristics of each of the links it uses to reach a destination through one or more preferred paths, and to report to its neighbors which links it has erased from its preferred paths. Using this information, each router constructs a source graph consisting of all the links it uses in the preferred paths to each destination. LVA ensures that the link-state information maintained at each router corresponds to the link constituency of the preferred paths used by routers in the network or internet. Each router runs a local algorithm or multiple algorithms on its topology table to compute its source graph with the preferred paths to each destination. Such algorithms can be any type of algorithm (e.g., shortest path, maximum-capacity path, policy path) and the only requirements for correct operation are for all routers to use the same algorithm to compute the same type of preferred paths, and that routers report all the links used in all preferred paths obtained. The disadvantage of LVA is that it may allow temporary routing loops to occur in the network or internetwork. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagram of two computer networks connected through a router. 
     FIG. 2 is a diagram of a number of computer networks connected by routers. In this figure, the routers are connected to each other by router-to-router links. 
     FIG. 3 is a block diagram of a typical router according to the present invention. Such routers will use a combination of hardware and software to perform packet-forwarding functions. 
     FIG. 4 illustrates the mechanism used in the feasibility condition called DMC defined below. This figure shows the relationship between various quantities maintained by the invention (and defined below) for a node i and a neighboring node k. These quantities include the distance RD j   k  reported in updates and queries sent by node k, the value of D jk   i* , and the value of FD j   k  as a function of time. The values of D jk   i*  reflect the values of RD j   k , but are offset in time because of propagation delays for messages traveling between node k and node i. The figure illustrates how DMC implies that FD j   k  &lt;D jk   i* . 
     FIG. 5 classifies the nodes in a network according to the state of the routing tables in nodes implementing the current invention. The region C j  consists of those nodes that have a path to destination j, and the region C j  contains those nodes that do not have a path to destination j. The sets shown in FIG. 5 have the following interpretation (the meaning of the terms active and passive are defined in the invention summary): 
     W j  contains nodes that are active and that have no successors. 
     A 1j  contains nodes that have successors. 
     A 2j  contains nodes that are passive and have no successors. Since these nodes must have a feasible distance of ∞, these nodes cannot be in the successor sets of any other nodes according to DMC. 
     As described in the invention summary below, with stable link costs and network topology, set W j  will eventually become empty. As a result, all nodes in C j  will have a path to the destination j and all nodes in C j  will be members of set A 2j  and consequently will have empty successor sets and infinite distance to the destination. 
     FIG. 6 illustrates how nodes may change their set membership from one set defined in FIG. 5 to another. 
     FIG. 7 shows a linear topology used in an example that shows the behavior of the present invention when link costs increase. 
     FIG. 8 shows a more complex topology used in an example that shows the behavior of the present invention when multiple link costs change before the routing tables converge. 
     SUMMARY OF THE INVENTION 
     The present invention provides for a feasibility condition that can be more easily met than the DIC, CSC, and SNC conditions, thus saving computational and network resources by avoiding unnecessary diffusing computations. The feasibility condition of the present invention is denoted as the DMC (Diffusing Multipath Condition), and is illustrated in FIG. 4. As with SNC, DMC assigns a feasible distance to each node, but unlike SNC, DMC increases this feasible distance at the end of a diffusing computation instead of the start of the diffusing computation. Unlike these previous feasibility conditions, DMC maintains an upper bound on the feasible distance of its neighbors based on the type of message sent. At node i, for destination j, and neighboring node k, this bound is denoted as D jk   i* . When a link from node i to node k is established or fails, or when node i initializes itself, D jk   i*  is set to ∞. Afterwards, D jk   i*  is set to the minimum distance received in a message from node k. When node i receives a query from node k, however, node i also keeps track of the minimum distance received from node k since the query. When node i sends node k a reply, node i sets D jk   i*  to the minimum distance received from node k since the query, decreasing D jk   i*  when a lower distance is reported in a message from node k as before. 
     DMC also requires that a node i never send a routing message containing a distance less than its feasible distance for the destination, that node i raises its feasible distance only when all its neighbors have replied to a query, and that node i raise its feasible distance for the destination no higher than the minimum distance sent in a message since the query and no higher than the distance in the query itself. In addition, when a node sends a query for a destination, it must not send a second query for that destination until it has received replies from all its neighbors. A link failure is treated as an implicit reply. 
     If the feasible distance at node i for destination j is denoted by FD j   i , and the feasible distance at node k for destination j is denoted as FD j   k , then DMC ensures that FD j   k  ≦D jk   i* . If node i chooses as its successor for destination j any node k such that D jk   i*  &lt;FD j   i , then it trivially follows that FD j   k  &lt;FD j   i  at every instant of time. If there were a loop, it would follow that FD j   i  &lt;FD j   i , which is impossible, so DMC ensures loop freedom at every instant of time. This has the added benefit of providing multipath routing of every instant of time, allowing paths with lengths longer than that of the shortest path. 
     The use of DMC leads to a reduction in diffusing computations over what is achievable in prior art systems. In particular, if node i receives a sequence of updates containing increasing distances, it may have to start a diffusing computation to raise its feasible distance even though it will not have to change its successors. With DMC, this diffusing computation may not be avoided because, as long as only updates are sent, node i can determine (using DMC) that its neighbors feasible distance has not increased. This can substantially reduce the number of routing messages sent through the network, leading to improved performance. 
     Because there is no need to freeze successors as there is in prior art systems, the present invention also provides a new mechanism for managing diffusing computations that is more efficient than the mechanisms used in prior art systems. This mechanism exploits DMC, which guarantees loop free paths at all instances of time. Given a destination j, a node i is said to be passive if it is not currently participating in a diffusing computation and is said to be active if it is participating in a diffusing computation. The successor set S j   i  of node i for destination j is defined as the set of neighboring nodes k for which D jk   i*  &lt;FD j   i . Diffusing computations are managed so as to obey the following constraints: 
     1. A passive node with no successors must have infinite feasible distance. 
     2. A node that has successors is not allowed to lower its feasible distance or send a reply to a node in its successor set if that would cause its successor set to empty unless that node has first raised its feasible distance to ∞. Node i may, however, have a finite feasible distance and also have no successors as a result of a topology change (e.g., a link failure). When this occurs, node i must become active. 
     3. An active node that has no successors and that has received the last reply to its query must (if necessary) send queries containing a distance of ∞. 
     4. A node that has sent a query, perhaps followed by updates, all containing a distance of ∞, must become passive when it receives its last reply to that query. 
     5. A node that receives a query from some node that is not in its successor set must sent that node a reply. 
     6. If a node can become passive when it receives the last reply to a query it must become passive. 
     These constraints imply the following. Suppose that there have been a sequence of topology changes in the network. After the last change, suppose that node i has a nonempty successor set. Since DMC prevents loops, if one follows the chain of successors, one must eventually reach either the destination or a node with no successors. The constraints ensure that a diffusing computation will eventually terminate, although a new diffusing computation may start. A node with no successors, however, must raise its feasible distance to ∞ by sending queries containing a distance of ∞. As a result, such nodes will eventually either obtain a successor or become passive with a distance of ∞ and no successors. Thus, eventually all nodes will either have a path to the destination or will be passive with no successors. This ensures that the computation always terminates. The relationship between nodes maintained by the present invention is illustrated in FIG. 5, which assigns nodes to various sets based on their state (active or passive) and the number of successors a node has. Transitions between these sets allowed by the present invention are illustrated in FIG. 6. 
     In addition, the constraints allow the following behavior: if an active node processes an update or link-state change that results in the shortest path to the destination satisfying its feasibility condition if all pending replies are sent, the node may send all of its replies. If the node is active, it becomes the root of a diffusing computation. This mechanism avoids the need to wait for diffusing computations to terminate before using new paths, and in addition, since replies will be sent earlier than otherwise, it allows diffusing computations to terminate quicker than is possible with prior art systems. 
     The present invention is also the first to provide multiple loop-free paths to destinations even when nodes are synchronizing their routing table update activities with other nodes. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A method and apparatus for distributed loop-free routing in computer networks will now be described. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be evident, however, to those skilled in the art that these specific details need not be used to practice the present invention. In other instances, well-known structures and circuit have not been shown in detail in order to avoid unnecessarily obscuring the present invention. 
     Turning to FIG. 1, a pair of computer networks are shown. These are connected through a router 500. Each computer network 100 includes a bus, ring, or other communications medium 200, and a number of attached computers 300. FIG. 2 shows a plurality of computer networks interconnected by routers. This configuration forms an internet. Lines shown connecting routers in FIG. 2 may be point-to-point connections or may be networks with additional computers attached. 
     FIG. 3 shows a block diagram of a typical router 500 according to the presently preferred embodiment. An internal data bus 503 connects a central processing unit (CPU) 505, a random access memory (RAM) 507, a read-only memory (ROM) 509 and multiple ports depicted at 511. Each individual port 513 is attached to a link 515 that in turn connects to another port of another router, or to a network. Data are sent and received through each of the ports 513. Data received from a port 513 are stored in the RAM 507, examined by the CPU 505, and sent out through a port 513 toward an appropriate destination. 
     Routing information is exchanged directly only between neighbors (adjacent routers) by means of routing messages; this is done either periodically, after routers detect changes in the cost or status of links, or after routers receive routing messages from neighbors. Each routing message contains a distance vector with one or more entries, and each entry specifies a distance to a given destination, an identifier specifying that destination, and an indication of whether the entry constitutes an update, query, or reply. The router hardware and software is responsible for ensuring that routing-message events and link-status events are delivered in the order in which they occur, that queries and replies are transmitted reliably, and that if a sequence of updates is transmitted, the last update is received. Providing hardware or software to meet this requirement is a well-understood application of communication protocol design. 
     The present invention provides an efficient method for determining the routing messages (of the type described above) to send in response to changes in link cost or status and in response to other routing messages, while providing loop-free paths to each destination and the shortest path to each destination upon convergence. This method can be described by an algorithm. Embodiments of this algorithm can use either hardware, software, or some combination. In addition, while the present invention is described in terms of a router, switches and other devices can also make use of routing information, and the present invention can be embodied purely in software, using locally available topology information. In this latter case, the computations for multiple nodes would be performed at one location instead of being distributed across a network. 
     The algorithm can be formally described by the following psuedocode description, which is based on the computer language Modula-II. We assume that a particular embodiment of the algorithm will provide a suitable definition for a cost (which is constrained to obey the rules of addition), a node ID (which indicates each addressable entity or range of entities in a network), and a representation of certain events (query, update, and reply for messages; linkdown, linkup, and linkchange for changes in link states). Certain functions are assumed to be provided by exporting them to software or hardware that monitors attached network interfaces. These functions are LinkUp, LinkDown, LinkChange, and Message. The embodiment is also assumed to provide a function, named Send in the psuedocode, that causes a list of events (updates, queries, and replies) to be sent in a data packet or sequence of packets that make up a routing message. The function Send is called at appropriate points. Mathematical notation is used instead of actual statements in a computer language because there are many ways in which the algorithm can be coded. Similarly, an append statement is used to add a routing-message event, represented as an ordered triple  type, destination, cost!, to a list of messages to be transmitted when Send is called. As stated above, these messages are to be delivered in the order provided. In the textual description of the invention, such triples are also used to describe routing-message events. 
     For notational convenience in the psuedocode, the index j always refers to the destination, the index i always refers to a particular node in the computer network, and the index m is the index associated with a link for which a change was detected. The index k is used to refer to some neighbor of node i. The following symbols represent the tables, indexed by identifiers (indicated by subscripts and superscripts) denoting various nodes in a network, that are used to describe the present invention: 
     N i  : the set of nodes or routers connected through a link with node i; a node in that set is said to be a neighbor of node i. 
     FD j   i  : is the feasible distance or feasible length at node i for destination j. 
     S j   i  : is the set of neighbors of node i that are used as successors of node i for destination j. This set represents the neighbors to use along all loop-free paths maintained by the routing-algorithm. 
     l k   i  : the cost or distance or length of a link in an event that changes the cost or status of a link. If a link fails, the cost is assumed to by ∞. This cost, length, or distance is also called the neighbor-node length. 
     D jk   i  : the distance reported by a neighbor in an update, query, or reply. This distance is also called the neighbor-to-destination length. 
     D jk   i*  : a table maintaining an upper bound on a neighbor&#39;s feasible distance. 
     D min   ij  : the cost of a path to destination j along the shortest path. 
     D jk   i*  : a table maintaining an upper bound on the feasible distance of a neighbor after a query from the neighbor is processed and before the following reply is sent. 
     RD j   i  : the cost for destination j that will be used in messages sent to neighbors. 
       j   i  : the last value of RD j   i  in a query or in an update that was broadcasted to all neighbors. 
     S jP1   i  : the value the successor set would have after an active-to-passive transition. 
     QS j   i  : the set of nodes for which a query has been received, but for which a reply has not been sent. One of the requirements for convergence is that QS j   i  .OR right.S j   i . 
     V i  : the set of all nodes or routers currently known to node i, excluding node i. 
     Z j   i  : the set of neighbors of node i that lie along a shortest path to destination j, or shortest-path set. 
     a j   i  : a flag that is true if node i is active for destination j. 
     r jk   i  : a flag that is true if node i has sent a query to node k for destination j but has not yet received a reply. 
     The operation of the invention can be described formally by psuedocode. As with any such description, there are various equivalent formulations that are obvious to someone skilled in the art. The psuedocode description is the following: 
     
         ______________________________________module RoutingAlgorithm;import procedure Send;          (* To transmit messages on lists *)import type NodeID, Cost;          (* Externally provided types *)import type Event;          (* Enum for message and link events: *)          (* query, update, replyfor messages; *)          (* else linkdown, linkup, linkchange. *)export LinkUp, LinkDown,LinkChange, Message;var l.sub.k.sup.i : Cost;          (* Cost of a link *)var D.sub.jk.sup.i : Cost;          (* Neighbor&#39;s reported distance *)var FD.sub.j.sup.i : Cost;          (* Feasible Distance *)var D.sub.jk.sup.i *: Cost;          (* Upper bound on neighbor&#39;s FD *)var D.sub.min.sup.ij : Cost;          (* minimum distance to destination *)var D.sub.jk.sup.i *: Cost;          (* D.sub.jk.sup.i * to use after replying *)var RD.sub.j.sup.i : Cost;          (* Distance to report to neighbors *)var RD.sub.j.sup.i : Cost;          (* Last transmitted RD.sub.j.sup.i  *)vars S.sub.j.sup.i : set of NodeID;          (* Successor Set *)var S.sub.jP1.sup.i : set of NodeID;          (* for passive S.sub.j.sup.i test *)var QS.sub.j.sup.i : set of NodeID;          (* Query Successor Set *)var N.sup.i : set of NodeID;          (* Neighboring nodes *)var V.sup.i : set of NodeID;          (* All nodes ≠ i currently known *)var Z.sub.j.sup.i : set of NodeID;          (* Neighbors along shortest paths *)var a.sub.j.sup.i : set of NodeID;          (* true when active *)var r.sub.jk.sup.i : boolean;          (* true if waiting for a reply *)procedure Common (j: NodeID);begin for all k ε N.sup.i do  if k ε QS.sub.j.sup.i then   D.sub.jk.sup.i * ← D.sub.jk.sup.i *; append  reply,j,RD.sub.j.sup.i ! to list k;  elsif RD.sub.j.sup.i ≠ RD.sub.j.sup.i then   append  update,j,RD.sub.j.sup.i ! to list k;  end; end; QS.sub.j.sup.i ← .0.; RD.sub.j.sup.i ← RD.sub.j.sup.i ;end Common;procedure MakeUpdates (j: NodeID);begin if RD.sub.j.sup.i ≠ RD.sub.j.sup.i then  for all k ε N.sup.i do   append  update,j,RD.sub.j.sup.i ! to list k;  end;  RD.sub.j.sup.i ← RD.sub.j.sup.i ; end;end MakeUpdates;procedure MakeQueries (j: NodeID);begin RD.sub.j.sup.i ← RD.sub.j.sup.i ; for all k ε {χ ε N.sup.i | l.sub.χ.sup.i ≠ ∞} do  r.sub.jk.sup.i ← true;  append  query,j,RD.sub.j.sup.i ! to list k; end; if (∀k ε N.sup.i):r.sub.jk .sup.i false thenFD.sub.j.sup.i = ∞ end;end MakeQueries;procedure SelectiveReply (e: Event; j, m: NodeID; c: Cost);(** Can be change to implement various policies for replying to* nodes in QS.sub.j.sup.i while active. *)begin if ord(QS.sub.j.sup.i) ≦ 1 then return end; if e = query Λ m ε QS.sub.j.sup.i then  QS.sub.j.sup.i ← QS.sub.j.sup.i - {k};  D.sub.jm.sup.i * ← D.sub.jm.sup.i *;  if D.sub.jm.sup.i * ≧ FD.sub.j.sup.i then   S.sub.j.sup.i ← S.sub.j.sup.i - {m}  end;  append  reply, j, RD.sub.j.sup.i ! to list m; end;end SelectiveReply;procedure ModifyTables (e: Event; j: NodeID; m: NodeID);begin a.sub.j.sup.i ← ((∃k) : r.sub.jk.sup.i = true); D.sub.min.sup.ij ← min{D.sub.jk.sup.i + l.sub.k.sup.i | kε N.sup.i }; D.sub.jm.sup.i * ← min(D.sub.jm.sup.i *,D.sub.jm.sup.i); Z.sub.j.sup.i ← {k ε N.sup.i | D.sub.jk.sup.i +l.sub.k.sup.i = D.sub.min.sup.ij Λ D.sub.min.sup.ij ≠∞}; if e = query then  D.sub.jm.sup.i * ← D.sub.jm.sup.i ;  if D.sub.jm.sup.i * ≧ FD.sub.j.sup.i then   D.sub.jm.sup.i * ← D.sub.jm.sup.i *; append  reply, j,RD.sub.j.sup.i ! to list m;  else QS.sub.j.sup.i ← QS.sub.j.sup.i ∪ {m};  end;elsif e = linkdown then  r.sub.jm.sup.i ← false; D.sub.jm.sup.i * ← ∞;D.sub.jm.sup.i * ← ∞;  N.sup.i ← N.sup.i - {m}; QS.sub.j.sup.i ← QS.sub.j.sup.i -{m}; elsif e = reply then r.sub.jm.sup.i ← false; D.sub.jm.sup.i *← min(D.sub.jm.sup.i *, D.sub.jm.sup.i); elsif m ε QS.sub.j.sup.i then D.sub.jm.sup.i *= min(D.sub.jm.sup.i *,D.sub.jm.sup.i); else D.sub.jm.sup.i * ← D.sub.jm.sup.i *; end; S.sub.j.sup.i ← {k ε N.sup.i | D.sub.jk.sup.i * &lt;FD.sub.j.sup.i }; S.sub.jP1.sup.i ← {k ε N.sup.i | D.sub.jk.sup.i *&lt; min(D.sub.min.sup.ij,FD.sub.j.sup.i)};end ModifyTables;procedure PassiveTransition(e: Event; j, m: NodeID; c: Cost);begin if Z.sub.j.sup.i ∩ S.sub.jP1.sup.i ≠ .0. then  RD.sub.j.sup.i ← D.sub.min.sup.ij ; S.sub.j.sup.i← S.sub.jP1.sup.i ; FD.sub.j.sup.i ← min(FD.sub.j.sup.i,D.sub.min.sup.ij);  Common (j);else  if S.sub.j.sup.i = .0. then RD.sub.j.sup.i ← ∞;  else RD.sub.j.sup.i ← Choose(e,j,m,c);  end;  if FD.sub.j.sup.i ≠ ∞ then MakeQueries(j);  else Common (j);  end; end;end PassiveTransition;procedure ActiveTransition (e: Event; j, m: NodeID; c: Cost);var S.sub.jP2.sup.i : set of NodeID;begin if Z.sub.j.sup.i ∩ S.sub.jP1.sup.i ≠ .0. Λ RD.sub.j.sup.i ≧ D.sub.min.sup.ij Λ ChoosePassive(e,j,m,c) then  FD.sub.j.sup.i ← min(FD.sub.j.sup.i,D.sub.min.sup.ij);  S.sub.j.sup.i ← S.sub.jP1.sup.i ; RD.sub.j.sup.i= D.sub.min.sup.ij ;  Common (j); else  if ∀ (k) : r.sub.jk.sup.i = false then   S.sub.jP2.sup.i ← {k ε N.sup.i | D.sub.jk.sup.i* &lt; min(D.sub.min.sup.ij,RD.sub.j.sup.i)};   if S.sub.jP2.sup.i ∩ Z.sub.j.sup.i ≠ .0. then    FD.sub.j.sup.i ← min(RD.sub.j.sup.i,D.sub.min.sup.ij);RD.sub.j.sup.i ← D.sub.min.sup.ij ;    S.sub.j.sup.i ← S.sub.iP2.sup.i ;    Common (j);   elsif RD.sub.j.sup.i = ∞ then    S.sub.j.sup.i ← S.sub.jP2.sup.i ; FD.sub.j.sup.i← D.sub.min.sup.ij ;    Common(j);   else    FD.sub.j.sup.i ← RD.sub.j.sup.i ;    S.sub.j.sup.i ← {k ε N.sup.i | D.sub.jk.sup.i *&lt; FD.sub.j.sup.i };    if S.sub.j.sup.i = .0. then RD.sub.j.sup.i = ∞;    else RD.sub.j.sup.i = min{D.sub.jk.sup.i + l.sub.k.sup.i | kε QS.sub.j.sup.i };    end;    MakeQueries (j);   end;  else SelectiveReply (e, j, m, c);  end; end; end ActiveTransition; procedure Transition (e: Event; j: NodeID; m: NodeID; c: Cost); begin  ModifyTables(e, j, m);  if a.sub.j.sup.i then ActiveTransition (e, j, m, c);  else PassiveTransition (e, j, m, c);  end; end Transition; procedure Init1; begin  N.sup.i ← .0.; V.sup.i ← .0.;  for all k ε {χ | l.sub.χ.sup.i &lt; ∞}  do   N.sup.i ← N.sup.i ∪ {χ};  end;  for all k ε {χ | l.sub.χ.sup.i &lt; ∞}  do   Init2 (k);  end;  RD.sub.i.sup.i ← 0; RD.sub.i.sup.i ← ∞;  MakeUpdates (i);  Send; end Init1; procedure Init2 (χ: NodeID); begin  V.sup.i ← V.sup.i ∪ {χ};  FD.sub.χ.sup.i ← ∞; RD.sub.χ.sup.i ← ∞;RD.sub.χ.sup.i ← ∞; D.sub.min.sup.iχ  ← ∞;  S.sub.χ.sup.i ← .0.; QS.sub.χ.sup.i ← .0.;  for all k ε N.sup.i  do   D.sub.χk.sup.i ← ∞; D.sub.χk.sup.i * ←∞; D.sub.χk.sup.i * ← ∞;   r.sub.χk.sup.i ← false;  end; end Init2; procedure LinkUp(m: NodeID; c: Cost); begin  l.sub.m.sup.i ← c; V ← V ∪ {m};  if m .epsilon slash. N.sup.i then   N.sup.i ← N.sup.i ∪ {m};   Init2 (m);  end;  append  update, i, RD.sub.i.sup.i ! to list m;  for all j ε N.sup.i do   D.sub.jm.sup.i ← ∞; D.sub.jm.sup.i * ← ∞;D.sub.jm.sup.i * ← ∞;   r.sub.jm.sup.i ← false;   if RD.sub.j.sup.i &lt; ∞ then    append  update, j, RD.sub.j.sup.i ! to list m;   end;  end;  Send; end LinkUp; procedure LinkDown(m: NodeID); begin  l.sub.m.sup.i ← ∞;  for all j ε V.sup.i do   D.sub.jm.sup.i = ∞;   Transition(linkdown, j, m, ∞);  end;  Send; end LinkDown; procedure Linkchange(m: NodeID; c: Cost); begin  l.sub.m.sup.i ← c;  for all j ε V.sup.i do   Transition(linkchange, j, m, c);  end;  Send; end LinkChange; procedure Message(e: Event; j: NodeID; m: NodeID; c: Cost); begin  if i = j Λ e = query then   append  reply, i, RD.sub.i.sup.i ! to list m;  elsif i ≠ j then   if j .epsilon slash. V.sup.i then    Init2 (j);   end;   D.sub.jm.sup.i ← c;   Transition (e, j, m, c);  end;  Send; end Message; function Choose(e: Event; j, m: NodeID; c: Cost): Cost; begin  if (e = linkdown Λ m = j) V (e = query Λ c = ∞)then   return ∞;  elsif QS.sub.j.sup.i ≠ .0. then   return min{D.sub.jk.sup.i + l.sub.k.sup.i | k εQS.sub.j.sup.i };  elsif {D.sub.jk.sup.i * ≦ FD.sub.j.sup.i } ≠ .0. then  return min{D.sub.jk.sup.i + l.sub.k.sup.i | D.sub.jk.sup.i *≦ FD.sub.j.sup.i }; else  return ∞; end; end Choose; function ChoosePassive(e: Event; j, m: NodeID; c: Cost): Boolean; begin  return QS.sub.j.sup.i ∪ {k ε Ni | D.sub.jk.sup.i * = ∞ } = .0.; end Choose Passive; begin  Init1; end RoutingAlgorithm.______________________________________ 
    
     The operation of the algorithm described by the above psuedocode is as follows. When a router i is turned on or the system otherwise initializes itself by setting RD i   i  to 0 and by setting N i , V i  to .0.. For all destinations j, S j   i , QS j   i , and Z j   i  are set to .0., and the values FD j   i , RD j   i , D min   ij , and  j   i  are set to ∞. For all destinations j and all neighbors k of router i, D jk   i , D jk   i* , and D jk   i*  are set to ∞, and the flag r jk   i  is set to false. If a destination or neighboring node is unknown, the corresponding entries do not exist are and not used. At this point, the router sends an routing-message event to all neighbors, containing the triple  update, i, 0! to advertise a distance of zero from itself. 
     The router then responds to messages and link events, and it is assumed that after initialization, a router will obtain a link-up event for every operational neighboring router k connected to the current router i by a functioning link. A router will also obtain a link-up event if a link that was previously not operational becomes operational. The events that can occur are link-up events, link-down events, link-cost-change events, and routing-message events. In the psuedocode, these are handled by the functions LinkUp, LinkDown, LinkChange, and Message respectively. These set a few table entries, and, except for LinkUp, call the function Transition. The function Transition takes four arguments--an indicator encoding the type of event (linkdown, linkchange, update, query, reply), a node id j for a destination, a node id m for the link associated with the event or message, and the cost associated with the event. The cost associated with the event is either the new link cost (if the event is linkdown or linkchange) or the distance reported in a routing-message event (if the event is update, query, or reply). The function Transition embodies behavior common to the processing of all events. As mentioned previously, a routing message consists of a vector of routing events. These routing events are processed in the order in which they occur in the routing message. The behavior of the invention is not dependent on how these events are grouped into messages, as long as the order in which they occur is preserved, both when received and when transmitted. 
     When a link-up event is processed by router i, the new neighbor m is added to the sets N i  and V i , and if the new neighbor was not previously in N i , then the following variables are initialized: S m   i , QS m   i , and Z m   i  are set to .0., and the values FD m   i , RD m   i , D min   im , and  m   i  are set to ∞. For all destinations j and all neighbors k of router i, D mk   i , D mk   i* , and D mk   i*  are set to ∞, and the flag r mk   i  is set to false. Next, a routing-message event  update, i, RD i   i  ! is queued for transmission to neighbor m, and for all destinations j, D jm   i , D jm   i* , and D jm   i*  are set to ∞, and the flag r jm   i  is set to false. In addition, for all destinations j, if RD j   i  &lt;∞, a routing-message event  update, j, RD j   i  ! is queued for transmission to node m. Finally, all queued routing-message events are sent. 
     When a link-down event is processed by router i, indicating that the link to neighbor m is not available, the link cost l m   i  is set to ∞, and for all destinations j, D jm   i  is set to ∞ and the function Transition(linkdown, j, m, ∞) is called. Then all queued routing-message events are sent. 
     When a link-change event is processed by router i, the link cost l m   i  is updated to reflect the new value c of the cost of the link from router i to neighboring router m. Then for every destination j, Transition(linkchange,j,m,c, is then called. Finally, all queued routing-message events are sent. 
     When a routing-message event is processed, the various field in the event are read to determine the event type e (update, query, or reply), the destination node ID j that appears in routing-message event, the neighboring node m that sent the routing-message event, and the distance c in the routing-message event. If j matches the node ID i of the current router, and the event type is query, then a reply routing-message event  reply, i, RD i   i  ! is queued for transmission to node m. Otherwise, there are two possibilities. The first is that the destination in the routing-message event matches the current router. For this case, the event is simply ignored. The second case is that the destination in the routing-message event does not match the current router. In this case, if j is a not member of V i , then we must initialize table entries: S j   i , QS j   i , and Z j   i  are set to .0., and the values FD j   i , RD j   i , D min   ij , and  j   i  are set to ∞; for all neighbors k of router i, D jk   i , D jk   i* , and D jk   i*  are set to ∞, and the flag r jk   i  is set to false. The second case continues by setting D jm   i  to c and then calling Transition(e, j, m, c). Finally (in both cases), all queued routing-message events are sent. 
     The function Transition(e, j, m, c) describes the handling of an event e (linkdown, linkchange, update, query, reply), for destination node ID j, in a routing message or link-cost/status change for neighbor m, with a new cost c. The function Transition starts by doing some preliminary table updates (describe in the psuedocode by the function ModifyTables) in the following sequence: 
     1. a flag a j   i  is set to true if the r jk   i  flag is true for any value of k, where k is the node ID of a neighbor of node i. While a flag is used in this description, any number of techniques are possible for tracking this information. 
     2. D min   ij  is updated to contain the minimum value of D jk   i  +l k   i  for all neighbors of router i. 
     3. D jm   i*  is updated to be the minimum of D jm   i*  and D jm   i . 
     4. Z j   i  is updated to contain the set of all neighboring nodes k for which D jk   i  +l k   i  =D min   ij , unless D min   ij  =∞ in which case Z j   i  becomes the empty set .0.. 
     5. If the event is a query, then the following sequence of operations are performed: 
     (a) D jm   i*  is set to D jm   i . 
     (b) If D jm   i*  ≧FD j   i , then D jm   i*  is set to D jm   i* . Then a routing-message event  reply, j, RD j   i  ! is queued for transmission to node m. 
     else if the event is a linkdown event, then the following sequence of operations are performed: 
     (a) r jm   i  is set to false. 
     (b) D jm   i*  and D jm   i*  are set to ∞. 
     (c) m is taken out of the sets N i  and QS j   i . 
     else if the event is a reply, then the following sequence of operations are performed: 
     (a) r jm   i  is set to false. 
     (b) D jm   i*  is set to the minimum of D jm   i*  and D jm   i . 
     else if m is a member of QS j   i , then D jm   i*  is set to the minimum of D jm   i*  and D jm   i , otherwise D jm   i*  is set to D jm   i* . 
     6. S j   i  is set to the set of neighboring nodes such that, for any neighbor k in this set, D jk   i*  is less than FD j   i . 
     7. A temporary variable S jP1   i , is set to the set of neighboring nodes such that for any neighbor k in this set, D jk   i*  is less than the minimum of D min   ij  and FD j   i . 
     After these preliminary operations, the function Transition uses the flag a j   i . If a j   i  is true, the current router i was in the active state when Transition was called, and if a j   i  is false, i was in the passive state when Transition was called. Transition behaves differently in each case. 
     In the case where a j   i  is true, Transition first performs a test to see (a) if the sets Z j   i  and S jP1   i  have any common members, (b) if RD j   i  is greater than D min   ij , and (c) if a function named ChoosePassive with arguments (e, j, m, c) obtained from Transition returns a value of true. If (a), (b), and (c) are all true, Transition sets FD j   i  to D min   ij  if this would decrease FD j   i , sets S j   i  to S jP1   i , sets RD j   i  to D min   ij , and calls the function Common defined in the psuedocode and described below to queue the appropriate routing-message events for transmission to neighboring nodes. If (a), (b), and (c) are not all true, Transition checks if there is any neighbor k for which r jk   i  is true. If one exists, Transition calls SelectiveReply(e, j, m, c), which is defined below. If one does not exist, Transition first sets a local variable S jP2   i  to the set of all neighboring nodes k such that D jk   i*  is less than the minimum of RD j   i  and D min   ij , and then makes the following mutually exclusive choices: 
     1. if S jP2   i  and Z j   i  have a common member, then the following steps are performed: 
     (a) FD j   i  is set to the minimum of RD j   i  and D min   ij . 
     (b) RD j   i  is set to D min   ij . 
     (c) S j   i  is set to S jP2   i . 
     (d) the function Common is called to queue routing-message events for transmission to neighboring nodes. 
     2. else if RD j   i  has a value of ∞, then the following steps are performed: 
     (a) S j   i  is set to S jP2   i . 
     (b) FD j   i  is set to D min   ij . 
     (c) the function Common is called to queue routing-message events for transmission to neighboring nodes. 
     3. otherwise, the following steps are performed: 
     (a) FD j   i  is set to RD j   i . 
     (b) S j   i  is set to the set of neighboring nodes such that for each neighbor k in the set, D jk   i*  is less than FD j   i . 
     (c) If S j   i  is empty (after the previous step), then RD j   i  is set to ∞, otherwise RD j   i  is set to the minimum value of D jk   i  +l k   i  out of all k that are members of the set QS j   i . 
     (d) The function MakeQueries(j) defined below is called to send routing-message events for destination j. 
     In the case where a j   i  is false, the function Transition checks if the sets Z j   i  and S jP1   i  have any common members. If they do, then the following sequence of events is performed: 
     1. RD j   i  is set to D min   ij , S j   i  is set to S jP1   i , and FD j   i  is set to D min   ij  if that would decrease FD j   i . 
     2. the function Common is called to queue routing-message events for transmission to neighboring nodes. 
     Otherwise, the following sequence of events is performed: 
     1. if S j   i  is empty, then RD j   i  is set to ∞, otherwise RD j   i  is set to the value returned by a call to the function Choose(e, j, m, c), where the arguments passed to Choose are the same ones passed to Transition. 
     2. If FD j   i  is not equal to ∞, then call MakeQueries(j), otherwise call Common(j). We note that j is the destination passed as an argument to Transition. 
     The functions MakeQueries(j) and Common(j) are simple utility functions to send messages. 
     MakeQueries(j) first sets the variable  j   i  to RD j   i  and then, for every neighbor k, MakeQueries sets r jk   i  to true and queues a routing-message event  query, j, RD j   i  ! for transmission to node k. If there are no available neighbors, the function MakeQueries sets F j   i  to ∞, as no messages can be sent and no neighbors can be reached. 
     Common(j) iterates over each neighboring node ID k in N i , and performs the following: 
     1. if k is a member of QS j   i  then D jk   i*  is set to D jk   i* , and the routing-message event  reply, j, RD j   i  ! is queued for transmission to node k. 
     2. otherwise if RD j   i  is not equal to  j   i , the routing-message event  update, j, RD j   i  ! is queued for transmission to node k. 
     Finally, Common sets QS j   i  to the empty set .0., and sets  j   i  to RD j   i . 
     The functionality provided by MakeQueries and Common can, of course, be easily provided by other means than a function. The current description provides these purely for clarity: Common shows how one can easily avoid sending additional updates when costs have not changed, and how one can send avoid sending duplicate replies. MakeQueries shows how one can handle the case where a node has no neighbors, and therefore needs to set its feasible distance to infinity. 
     The functions Choose, SelectiveReply, and ChoosePassive are used in the current description to explicitly illustrate various choices that can be made, and in practice would not necessarily be provided by functions in a programming language. Various semantics for Choose, SelectiveReply, and ChoosePassive are possible. The current definitions are the best known to date, although known alternatives provide only slightly worse performance. To summarize the behavior of these functions, we note that 
     SelectiveReply keeps one outstanding query in QS j   i . If a second query arrives during an active phase, a reply will be sent for that query. 
     Choose returns ∞ if a diffusing computation is started by a linkdown event, or if a diffusing computation is started with a query reporting ∞. Otherwise if QS j   i  ≠.0., it chooses min{D jk   i  +l k   i  |kεQS j   i  }, else min{D jk   i  +l k   i  |kεN i  D jk   i*  ≦FD j   i  }. 
     ChoosePassive returns true if {k εQS j   i  |D jk   i*  =∞}=.0. and false otherwise. 
     An alternative for SelectiveReply is for SelectiveReply to do nothing. In this case, while convergence will be slower, this choice for SelectiveReply will ensure that, if the current nodes wishes to delete an entry, that all upstream nodes will have been notified before the current node delete&#39;s its entry. In some applications (e.g., providing shortcut routes in a bridged network), this property may be necessary for correct operation. 
     Embodiment in a Network Simulator 
     One existing embodiment of the invention is in a network simulator. The simulator uses small integers as node IDs instead of a network address (e.g., an IP address), so that tables can be implemented as arrays instead of hash tables or other data structures. Such simplifications are not significant, and the simulator does in fact contain an actual implementation of the current invention. This simulator was used to generate the tables shown in the examples in the next section. 
     Examples of Operation 
     The following examples, each for a different topology and different sequence of link changes, show the sequence of changes to variables defined in the formal description shown above. The state of each node at the start of an example or at the end of an example is called a snapshot. In between, the example provides entries at each time (measured in arbitrary units) showing (a) what routing-message events or link events a node received, and (b) what messages the node sent in response, and (c) the new state of the node. The state of the node i is described by the following arrays and tables. The arrays, whose index is the destination j given in square brackets, are named as follows: 
     1. dist denotes the value of D min   ij . 
     2. repldist denotes the value of RD j   i . 
     3. repldisttilde denotes the value of  j   i . 
     4. FD denotes the value of FD j   i . 
     5. DMin denotes the value of D min   ij . 
     6. successor denotes a successor along the shortest path. 
     The tables are represented by a series of rows. The columns are defined as follows: 
     1. dest denotes the destination (i.e., node j). 
     2. neighbor denotes a neighboring node k. 
     3. dist denotes the value of D jk   i . 
     4. dist* denotes the value of D jk   i* . 
     5. dist*.sup.  denotes the value of D jk   i* . 
     6. r denotes the value of r jk   i . 
     7. inS indicates if the entry in the neighbor column is a member of the set S j   i . The value T indicates that it is a member and a value of F indictes that it is not a member. 
     8. inQS indicates if the entry in the neighbor column is a member of the set QS j   i . The value T indicates that it is a member and a value of F indictes that it is not a member. 
     9. inZ indicates if the entry in the neighbor column is a member of the set Z j   i . The value T indicates that it is a member and a value of F indictes that it is not a member. 
     10. lcost denotes the cost of the link connecting the current node to a neighbor (the one listed in the neighbor column on the current row. 
     The first example shows a linear topology, illustrated in FIG. 7, with 6 nodes (n 1  to n 6 ) in which initially all links have a cost of 1.0. Next, link (n 1 , n 2 ) increases its cost to 1.5, and the routing tables are allowed to converge. At this point, the state of all the nodes are shown in the following trace. The cost of link (n 1 , n 2 ) is then increased to 2.0, and the behavior of each node is displayed. Once the routing tables are stable, the state of each node is printed. For simplicity, node n 1  is the only destination shown. The first event shown occurs at time 11 because of the time required to reach the initial state for the example. Messages are assumed to take one time unit to propagate from one node to its neighbors. 
     
         __________________________________________________________________________Elapsed time = 6Elapaed time = 5Snapshot for node n1:dist n1! = 0repldist nl! = 0repldisttilde nl! = 0FD n1! = 0Dmin n1! = infinitysuccessor n1! = n1 (which is the destination)Tables.    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcostSnapshot for node n2:dist n1! = 1.5repldist n1! = 1.5repldisttilde n1! = 1.5FD n1! = 1Dmin n1! = 1.5successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1.5    n1 n3   2.5               2  2  F F F  F  1Snapshot for node n3:dist n1! = 2.5repldist n1! = 2.5repldisttilde n1! = 2.5FD n1! = 2Dmin n1! = 2.5successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1.5               1  1  F T F  T  1    n1 n4   3.5               3  3  F F F  F  1Snapshot for node n4:dist n1! = 3.5repldist n1! = 3.5repldisttilde n1! = 3.5FD n1! = 3Dmin n1! = 3.5successor n1! = n3Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   2.5               2  2  F T F  T  1    n1 n5   4.5               4  4  F F F  F  1Snapshot for node n5:dist n1! = 4.5repldist n1! = 4.5repldisttilde n1! = 4.5FD n1! = 4Dmin n1! = 4.5successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n4   3.5               3  3  F T F  T  1    n1 n6   5.5               5  5  F F F  F  1Snapshot for node n6:dist n1! = 5.5repldist n1! = 5.5repldisttilde n1! = 5.5FD n1! = 5Dmin n1! = 5.5successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   4.5               4  4  F T F  T  1At time 11 node n1 calls procedure Change:(cost of link from n1 to n2 changing to 2)New State for node n1dist n1! = 0repldist n1! = 0repldisttilde n1! = 0FD n1! = 0Dmin n1! = infinitysuccessor n1! = n1 (which is the destination)Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcostAt time 11 node n2 calls procedure Change:(cost of link from n2 to n1 changing to 2)       sending  update, n1, 2! to n1       sending  update, n1, 2! to n3New State for node n2dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  2    n1 n3   2.5               2  2  F F F  F  1at time 12, n1 ignoring n2 from update because received at destinationNew State for node n1dist n1! = 0repldist n1! = 0repldisttilde n1! = 0FD n1! = 0Dmin n1! = infinitysuccessor n1! = n1 (which is the destination)Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcostat time 12, n3 received update from n2: dest = n1, dist = 2       sending  update, n1, 3! to n2       sending  update, n1, 3! to n4New State for node n3dist n1! = 2.5repldist n1! = 3repldisttilde n1! = 3FD n1! = 2Dmin n1! = 3successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   2  1  1  F T F  T  1    n1 n4   3.5               3  3  F F F  F  1at time 13, n2 received update from n3: dest = n1, dist = 3New State for node n2dist n1! = 2repldist n1! = 2repldisttilde R1! = 2FD n1! = 1Dmin n1! = 2successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  2    n1 n3   3  2  2  F F F  F  1at time 13, n4 received update fron n3: dest = n1, dist = 3       sending  update, n1, 4! to n3       sending  update, n1, 4! to n5New State for node n4dist n1! = 3 5repldist n1! = 4repldisttilde n1! = 4FD n1! = 3Dmin n1! = 4successor n1! = n3Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   3  2  2  F T F  T  1    n1 n5   4.5               4  4  F F F  F  1at time 14, n3 received update from n4: dest = n1, dist = 4New State for node n3dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 2Dmin n1! = 3successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   2  1  1  F T F  T  1    n1 n4   4  3  3  F F F  F  1at time 14, n5 received update from n4: dest = n1, dist = 4       sending  update, n1, 5! to n4       sending  update, n1, 5! to n6New State for node n5dist n1! = 4.5repldist n1! = 5repldisttilde n1! = 5FD n1! = 4Dmin n1! = 5successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n4   4  3  3  F T F  T  1    n1 n6   5.5               5  5  F F F  F  1at time 15, n4 received update fron n5: dest = n1, dist = 5New State for node n4dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 3Dmin n1! = 4successor n1! = n3Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   3  2  2  F T F  T  1    n1 n5   5  4  4  F F F  F  1at time 15, n6 received update from n5: dest = n1, dist = 5       sending  update, n1, 6! to n5New State for node n6dist n1! = 5.5repldist n1! = 6repldisttilde n1! = 6FD n1! = 5Dmin n1! = 6successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   5  4  4  F T F  T  1at time 16, n5 received update from n6: dest = n1, dist = 6New State for node n5dist n1! = 5repldist n1! = 5repldisttilde n1! = 5FD n1! = 4Dmin n1! = 5successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n4   4  3  3  F T F  T  1    n1 n6   6  5  5  F F F  F  1Elapsed time = 5Snapshot for node n1:dist n1! = 0repldist n1! = 0repldisttilde n1! = 0FD n1! = 0Dmin n1! = infinitysuccessor n1! = n1 (which is the destination)Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcostSnapshot for node n2:dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 1Dmin n1! = 2successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  2    n1 n3   3  2  2  F F F  F  1Snapshot for node n3:dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 2Dmin n1! = 3successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   2  1  1  F T F  T  1    n1 n4   4  3  3  F F F  F  1Snapshot for node n4:dist n1! = 4repldist  n1! = 4repldisttilde n1! = 4FD n1! = 3Dmin n1! = 4successor n1! = n3Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   3  2  2  F T F  T  1    n1 n5   5  4  4  F F F  F  1Snapshot for node n5:dist n1! = 5repldist n1! = 5repldisttilde n1! = 5FD n1! = 4Dmin n1! = 5successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n4   4  3  3  F T F  T  1    n1 n6   6  5  5  F F F  F  1Snapshot for node n6:dist n1! = 6repldist n1! = 6repldisttilde n1! = 6FD n1! = 5Dmin n1! = 6successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   5  4  4  F T F  T  1__________________________________________________________________________ 
    
     The above example shows that a node can see increasing link costs and using the present invention, only updates will be needed, so there are no diffusing computations. Prior art systems using SNC would in this case require a diffusing computation. 
     The second example shows a topology, illustrated in FIG. 8, in which initially all links have a cost of 1.0 except link (n 2 ,n 4 ), which has a cost of 3.0. At this point, the state of all nodes are shown in the following trace. Then the cost of link (n 2 , n 3 ) increases from 1.0 to 5.0. A half time unit later, the cost of link (n 2 , n 4 ) decreases from 3.0 to 1.0. The behavior of each node is shown until the routing tables converge. At this point, all the tables are printed to show the final state. The first event shown occurs at time 5.0 because of the time required to reach the initial state for the example. Subsequent events are spaced by 0.5 time units because of the starting time for the second link-cost change. Messages are assumed to take one time unit to propagate from one node to its neighbors. 
     
         __________________________________________________________________________Elapsed time = 5Snapshot for node n1:dist n1! = 0repldist n1! = 0repldisttilde n1! = 0FD n1! = 0Dmin n1! = infinitysuccessor n1! = n1 (which is the destination)Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcostSnapshot for node n2:dist n1! = 1repldist n1! = 1repldisttilde n1! = 1FD n1! = 1Dmin n1! = 1successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1    n1 n3   2  2  2  F F F  F  1    n1 n4   4  4  4  F F F  F  3Snapshot for node n3:dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  T  1    n1 n5   3  3  3  F F F  F  1Snapshot for node n4:dist n1! = 4repldist  n1! = 4repldisttilde n1! = 4FU n1! = 4Dmin n1! = 4successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  T  3    n1 n5   3  3  3  F T F  T  1Snapshot for node n5:dist n1! = 3repldist n1! = 3repldissttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n3Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   2  2  2  F T F  T  1    n1 n4   4  4  4  F F F  F  1    n1 n6   4  4  4  F F F  F  1Snapshot for node n6:dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   3  3  3  F T F  T  1    n1 n7   5  5  5  F F F  F  1Snapshot for node n7:dist n1! = 5repldist n1! = 5repldisttilde n1! = 5FD n1! = 5Dmin n1! = 5successor n1! = n8Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n6   4  4  4  F T F  T  1    n1 n5   4  4  4  F T F  T  1Snapshot for node n8:dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n9Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n7   5  5  5  F F F  F  1    n1 n9   3  3  3  F T F  T  1Snapshot for node n9:dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n10Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n8   4  4  4  F F F  F  1    n1 n10  2  2  2  F T F  T  1Snapshot for node n10:dist n1! = 2repldist  n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n9   3  3  3  F F F  F  1    n1 n1   0  0  0  F T F  T  2At time 5 node n2 calls procedure Change:(cost of link from n2 to n3 changing to 5)New State for node n2dist n1! = 1repldist n1! = 1repldisttilde n1! = 1FD n1! = 1Dmin n1! = 1successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1    n1 n3   2  2  2  F F F  F  5    n1 n4   4  4  4  F F F  F  3At time 5 node n3 calls procedure Change:(cost of link from n3 to n2 changing to 5)       broadcasting  query, n1, 6! to all neighborsNew State for node n3dist n1! = 6repldist n1! = 6repldisttilde n1! = 6FD n1! = 2Dmin n1! = 4successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  T T F  F  5    n1 n5   3  3  3  T F F  T  1At time 5.5 node n2 calls procedure Change:(cost of link fron n2 to n4 changing to 1)New State for node n2dist n1! = 1repldist n1! = 1repldisttilde n1! = 1FD n1! = 1Dmin n1! = 1successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1    n1 n3   2  2  2  F F F  F  5    n1 n4   4  4  4  F F F  F  1At time 5.5 node n4 calls procedure Change:(cost of link fron n4 to n2 changing to 1)       sending  update, n1, 2! to n2       sending  update, n1, 2! to n5New State for node n4dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  T  1    n1 n5   3  3  3  F F F  F  1at time 6, n2 received query from n3: dest = n1, dist = 6       sending  reply, n1, 1! to n3New State for node n2dist n1! = 1repldist n1! = 1repldisttilde n1! = 1FD n1! = 1Dmin n1! = 1successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1    n1 n3   6  6  6  F F F  F  5    n1 n4   4  4  4  F F F  F  1at time 6, n5 received query from n3: dest = n1, dist = 6       broadcasting  query, n1, 7! to all neighborsNew State for node n5dist n1! = 3repldist n1! = 7repldisttilde n1! = 7FD n1! = 3Dmin n1! = 5successor n1! = n3Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   6  2  6  T T T  F  1    n1 n4   4  4  4  T F F  T  1    n1 n6   4  4  4  T F F  T  1at time 6.5, n2 received update from n4: dest = n1, dist = 2New State for node n2dist n1! = 1repldist n1! = 1repldisttilde n1! = 1FD n1! = 1Dmin n1! = 1successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1    n1 n3   6  6  6  F F F  F  5    n1 n4   2  2  2  F F F  F  1at time 6.5, n5 received update from n4: dest = n1, dist = 2       sending  reply, n1, 3! to n3       sending  update, n1, 3! to n4       sending  update, n1, 3! to n6New State for node n5dist n1! = 7repldist  n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n3Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   6  6  6  T F F  F  1    n1 n4   2  2  2  T T F  T  1    n1 n6   4  4  4  T F F  F  1at time 7, n3 received reply from n2: dest = n1, dist = 1New State for node n3dist n1! = 6repldist  n1! = 6repldisttilde n1! = 6FD n1! = 2Dmin n:1! = 4successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  F  5    n1 n5   3  3  3  T F F  T  1at time 7, n4 received query from n5: dest = n1, dist = 7       sending  reply, n1, 2! to n5New State for node n4dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  T  1    n1 n5   7  7  7  F F F  F  1at time 7, n6 received query from n5: dest = n1, dist = 7broadcasting  query, n1, 8! to all neighborsNew State for node n6dist n1! = 4repldist n1! = 8repldisttilde n1! = 8FD n1! = 4Dmin n1! = 6successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   7  3  7  T T T  F  1    n1 n7   5  5  5  T F F  T  1at time 7, n3 received query from n5: dest = n1, dist = 7       sending  reply, n1, 6! to n5New State for node n3dist n1! = 6repldist n1! = 6repldisttilde n1! = 6FD n1! = 2Dmin n1! = 6successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  T  5    n1 n5   7  7  7  T F F  F  1    at time 7.5, n3 received reply from n5: dest = n1, dist = 3       sending  update, n1, 4! to n2       sending  update, n1, 4! to n5New State for node n3dist n1! = 6repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n2Table    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  F  5    n1 n5   3  3  3  F T F  T  1at time 7.5, n4 received update from n5: dest = n1, dist = 3New State for node n4dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  T  1    n1 n5   3  3  3  F F F  F  1at time 7.5, n6 received update from n5: dest = n1, dist = 3       sending  reply, n1, 4! to n5       sending  update, n1, 4! to n7New State for node n6dist n1! = 8repldist  n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   3  3  3  T T F  T  1    n1 n7   5  5  5  T F F  F  1at time 8, n5 received reply from n4: dest = n1, dist = 2New State for node n5dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   6  6  6  T F F  F  1    n1 n4   2  2  2  F T F  T  1    n1 n6   4  4  4  T F F  F  1at time 8, n7 received query from n6: dest = n1, dist = 8sending  reply, n1, 5! to n6New State for node n7dist n1! = 5repldist n1! = 5repldisttilde n1! = 5FD n1! = 5Dmin n1! = 5successor n1! = n8Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n6   8  8  8  F F F  F  1    n1 n8   4  4  4  F T F  T  1at time 8, n5 received query from n6: dest = n1, dist = 8       sending  reply, n1, 3! to n6New State for node n5dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   6  6  6  T F F  F  1    n1 n4   2  2  2  F T F  T  1    n1 n6   8  8  8  T F F  F  1at time 8, n5 received reply from n3: dest = n1, dist = 6New State for node n5dist n1! = 3repldist n1! = 3repldiisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   6  6  6  F F F  F  1    n1 n4   2  2  2  F T F  T  1    n1 n6   8  8  8  T F F  F  1at time 8.5, n2 received update from n3: dest = n1, dist = 4New State for node n2dist n1! = 1repldist n1! = 1repldisttilde n1! = 1FD n1! = 1Dmin n1! = 1successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1    n1 n3   4  4  4  F F F  F  5    n1 n4   2  2  2  F F F  F  1at time 8.5, n2 received update from n3: dest = R1, dist = 4New State for node n5dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n4Table    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   4  4  4  F F F  F  1    n1 n4   2  2  2  F T F  T  1    n1 n6   8  8  8  T F F  F  1at time 8.5, n7 received update from n6: dest = n1, dist = 4New State for node n7dist n1! = 5repldist n1! = 5repldisttilde n1! = 5FD n1! = 5Dmin n1! = 5successor n1! = n8Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n6   4  4  4  F T F  T  1    n1 n8   4  4  4  F T F  T  1at time 8.5, n5 received reply from n6: dest = n1, dist = 4New State for node n5dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   4  4  4  F F F  F  1    n1 n4   2  2  2  F T F  T  1    n1 n6   4  4  4  F F F  F  1at time 9, n6 received reply from n7: dest = n1, dist = 5New State for node n6dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   3  3  3  T T F  T  1    n1 n7   5  5  5  F F F  F  1at time 9, n6 received reply from n5: dest = n1, dist = 3New State for node n6dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n5Table    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   3  3  3  F T F  T  1    n1 n7   5  5  5  F F F  F  1Total messages sent = 21Total steps summed over all nodes = 25Total operations summed over all nodes = 25for node iterations for message with dest n1, max = 7, mean = 2.1 +-2.16564for node iterations with link change, max = 2, mean = 0.4 +- 0.663325Distribution of node iterations by dest: 4 0 2 2 1 0 0 1Number of nondeterministic successor choices = 0Elapsed time = 4Snapshot for node n1:dist n1! = 0repldist n1! = 0repldisttilde n1! = 0FD n1! = 0Dmin n1! = infinitysuccessor n1! = n1 (which is the destination)Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcostSnapshot for node n2:dist n1! = 1repldist n1! = 1repldisttilde n1! = 1FD n1! = 1Dmin n1! = 1successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n1   0  0  0  F T F  T  1    n1 n3   4  4  4  F F F  F  5    n1 n4   2  2  2  F F F  F  1Snapshot for node n3:dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor R1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  F  5    n1 n5   3  3  3  F T F  T  1Snapshot for node n4:dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n2Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n2   1  1  1  F T F  T  1    n1 n5   3  3  3  F F F  F  1Snapshot for node n5:dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n4Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n3   4  4  4  F F F  F  1    n1 n4   2  2  2  F T F  T  1    n1 n6   4  4  4  F F F  F  1Snapshot for node n6:dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n5Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n5   3  3  3  F T F  T  1    n1 n7   5  5  5  F F F  F  1Snapshot for node n7:dist n1! = 5repldist n1! = 5repldisttilde n1! = 5FD n1! = 5Dmin n1! = 5successor n1! = n8Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n6   4  4  4  F T F  T  1    n1 n8   4  4  4  F T F  T  1Snapshot for node n8:dist n1! = 4repldist n1! = 4repldisttilde n1! = 4FD n1! = 4Dmin n1! = 4successor n1! = n9Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n7   5  5  5  F F F  F  1    n1 n9   3  3  3  F T F  T  1Snapshot for node n9:dist n1! = 3repldist n1! = 3repldisttilde n1! = 3FD n1! = 3Dmin n1! = 3successor n1! = n10Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n8   4  4  4  F F F  F  1    n1 n10  2  2  2  F T F  T  1Snapshot for node n10:dist n1! = 2repldist n1! = 2repldisttilde n1! = 2FD n1! = 2Dmin n1! = 2successor n1! = n1Tables    dest       neighbor            dist               dist*                  dist*.sup.-                     r inS                         inQS                            inZ                               lcost    n1 n9   3  3  3  F F F  F  1    n1 n1   0  0  0  F T F  T  2__________________________________________________________________________ 
    
     The above example illustrates how new routes can be used immediately, and how a diffusing computation can be effectively canceled. This reduces running time compared to prior art systems based on SNC--for these systems, n 5  would have to wait for all upstream nodes to finish their diffusing computations before the new path could be used. Thus, the present invention provides faster convergence and better use of network resources.