Patent Publication Number: US-11658869-B2

Title: Method and apparatus for configuring a communication network using a connectivity metric

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is the first application filed for this invention. 
     FIELD OF THE INVENTION 
     The present invention pertains in general to communication networks, such as satellite networks, and in particular to a method and apparatus for configuring (e.g. initially configuring or reconfiguring) a communication network, for example by configuring nodes thereof. 
     BACKGROUND 
     Terrestrial networks are designed and deployed based on geographic locations. In such terrestrial networks, routers are often installed based on user demand and optical connections are installed to accommodate load and the routers&#39; shortest path behavior. Equipment failures are repaired quickly by maintenance personnel who can access the equipment at the site. 
     In contrast, in a satellite network, network nodes (e.g. routers) will likely be deployed in a regular geometric mesh in Earth orbit. Orbital locations will likely be precisely defined in order to enable inter-satellite links. 
     Failures in a satellite network are expected to be difficult to repair. A satellite-based failed piece of equipment would have to be captured for repair. Alternatively, the satellite could be left in orbit until it no longer provides any service. At this point, the satellite could be de-orbited and a replacement satellite launched. 
     The above methods of dealing with partial or full failures of satellite network nodes are expensive and problematic. Therefore there is a need to provide a method and apparatus that obviates or mitigates one or more limitations of the prior art. 
     This background information is provided to reveal information believed by the applicant to be of possible relevance to the present invention. No admission is necessarily intended, nor should be construed, that any of the preceding information constitutes prior art against the present invention. 
     SUMMARY 
     An object of embodiments of the present invention is to provide a method, apparatus and system for configuring (e.g. initially configuring or reconfiguring) a communication network, for example by configuring or reconfiguring nodes thereof. The configuring is based at least in part on a connectivity metric which is indicative of an extent to which nodes of the network are interconnected via links. The connectivity metric can be based on a Laplacian matrix which represents the interconnections between nodes of the network. In particular, a network configuration is selected, from among a plurality of potential implementations, based on the connectivity metric and obtained available information about the network. The selected network configuration is then implemented. 
     Embodiments of the present invention provide for a method and apparatus for reconfiguring a network, such as a satellite network, for example following failure events. This allows network operators to achieve an improved use of network resources throughout the operational life of such resources. Embodiments of the present invention can be applied to networks including satellites in low earth orbit or another type of orbit. Embodiments of the present invention can be more generally applied to any network with a regular structure, for example, of node locations. 
     In order to effectively reconfigure the network, there is provided a means to evaluate the network configuration. Embodiments of the present invention use “connectivity metrics” to evaluate the network configuration. This allows the network to be reconfigured from a state corresponding to a poor connectivity metric, to a state corresponding to a better connectivity metric, after a failure event occurs. A connectivity metric generally provides a numerical value, or set of values, which reflect the extent to which network nodes are interconnected with one another. For example, networks having nodes which are connected via more possible paths may be considered more interconnected than networks having nodes which are connective via fewer possible paths. Several particular connectivity metrics are described herein. 
     Embodiments of the present invention combine particular connectivity metrics with one or more search methods for determining network configurations, the search methods using the connectivity metrics. Embodiments of the present invention are applied in the context of a satellite operations, administration and maintenance (OAM) system. 
     According to embodiments of the present invention, there is provided a method for configuring a communication network. The method includes obtaining information indicative of current status of nodes of the communication network, links between the nodes of the communication network or a combination thereof. The method further includes processing the information to determine a network configuration based on the obtained information. The network configuration is implementable in the communication network by adjusting one or more of the nodes, one of more of the links between the nodes, or a combination thereof. The processing includes evaluating at least the network configuration based on a connectivity metric indicative of an extent to which the nodes are interconnected via the links. The method further includes providing instructions directing one or more underlying resources to implement the network configuration. 
     In some embodiments the network is a satellite network. In some embodiments the satellite network includes a low-earth orbit (LEO) satellite constellation, a plurality of LEO satellite constellations, a hybrid satellite constellation comprising LEO satellites and medium earth orbit (MEO) satellites, or a hybrid satellite constellation comprising LEO satellites and geostationary earth orbit (GEO) satellites. 
     In some embodiments the current status is indicative of whether or not one or more of the nodes or one or more of the links is in an outage state. 
     In some embodiments processing the information to determine the network configuration includes performing an optimization routine having an objective which is based on a connectivity metric. The connectivity metric is indicative of an extent to which said nodes are interconnected via said links. For example, the optimization routine can involve evaluating one or more candidate network configurations based on the connectivity metric, and selecting the network configuration as one of the candidate network configurations. The selected network configuration can be selected as the one having the highest amount of connectivity among candidates. Alternatively the selected network configuration can be selected as one (out of possibly several candidates) having at least a sufficient amount of connectivity (e.g. greater than a given required threshold) based on the connectivity metric. 
     In some embodiments the connectivity metric is based at least in part on one or more eigenvalues of a representative matrix, such as a Laplacian matrix or an adjacency matrix. The representative matrix is indicative of one of the candidate configurations. Evaluating the one of the candidate configurations includes computing the eigenvalues. In some embodiments the connectivity metric is based at least in part on a second smallest eigenvalue of the representative matrix. In some embodiments the connectivity metric is based at least in part on two or more eigenvalues of the representative matrix. In some embodiments the connectivity metric is based at least in part on all eigenvalues of the representative matrix. In some embodiments the two or more eigenvalues of the representative matrix, or all eigenvalues of the representative matrix, are expressed as a vector value or as a scalar value encoding the eigenvalues. When embodiments of the present invention are discussed herein with respect to the Laplacian matrix, it should be understood that another form of representative matrix can potentially be substituted for the Laplacian matrix. 
     In some embodiments the connectivity metric indicates connectivity, Cheeger number, or algebraic connectivity, or graph spectra. In some embodiments, the connectivity metric is determined based on one or more spectral analysis operations applied to a representative matrix which encodes the interconnections between network nodes in accordance with a graph theoretic representation. 
     In some embodiments processing the information to determine the network configuration includes evaluating a plurality of candidate network configurations based on the connectivity metric using a tree search, and selecting the network configuration and one of the candidate network configurations evaluated using the tree search and having at least a sufficient amount of connectivity based on the connectivity metric. The tree search is performed on a tree having a root node, a plurality of branch nodes and a plurality of leaf nodes, each branch node and leaf node representing one of the candidate network configurations, and adjacent pairs of the branch nodes and leaf nodes representing candidate network configuration which differ by an incremental amount. In some embodiments the tree search is a depth-first tree search. 
     In some embodiments processing the information to determine the network configuration includes training a machine learning agent to select, from among candidate network configuration, an adequately connected network configuration, the training including providing feedback to the machine learning agent. The feedback is based at least in part on the connectivity metric. Processing the information further includes operating the machine learning agent to select the network configuration based on the information indicative of the current status of nodes of the communication network, the links between the nodes of the communication network, or the combination thereof. In some embodiments the machine learning agent uses a neural network to evaluate a state action value function indicative of the feedback to the machine learning agent. 
     In some embodiments the network configuration includes configuring one or more nodes. 
     In some embodiments the network configuration includes physically reorienting one or more of the nodes to reorient one of more directional transceivers thereof, the reorienting of directional transceivers affecting one or more of the links between the nodes. 
     According to embodiments of the present invention, there is provided a device, such as an electronic computing device which may be deployed on ground or alternatively aboard a satellite. The device includes a network interface, a processor, and a non-transient computer readable memory having stored instructions which when executed by the processor configure the device to execute the methods disclosed herein. In various embodiments, such a device is configured to obtain information indicative of current status of nodes of the communication network, links between the nodes of the communication network or a combination thereof. The device is further configured to process the information to determine a network configuration based on the obtained information. The network configuration is implementable in the communication network by adjusting one or more of the nodes, one or more of the links between the nodes, or a combination thereof. The processing comprises evaluating at least the network configuration based on a connectivity metric. The connectivity metric is indicative of an extent to which the nodes are interconnected via the links. The device is further configured to provide instruction directing one or more underlying resources to implement the network configuration. 
     Embodiments have been described above in conjunctions with aspects of the present invention upon which they can be implemented. Those skilled in the art will appreciate that embodiments may be implemented in conjunction with the aspect with which they are described, but may also be implemented with other embodiments of that aspect. When embodiments are mutually exclusive, or are otherwise incompatible with each other, it will be apparent to those skilled in the art. Some embodiments may be described in relation to one aspect, but may also be applicable to other aspects, as will be apparent to those of skill in the art. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       Further features and advantages of the present invention will become apparent from the following detailed description, taken in combination with the appended drawings, in which: 
         FIG.  1    illustrates an example system including satellites and a device for configuring same, according to an embodiment of the present invention. 
         FIGS.  2 A and  2 B  illustrate network nodes located in a geometric mesh, and reconfiguration of the network nodes in view of a failure, according to an embodiment of the present invention. 
         FIG.  3    illustrates operations for configuring a communication network, according to an embodiment of the present invention. 
         FIG.  4    illustrates a network configuration apparatus, according to an embodiment of the present invention. 
         FIGS.  5 A,  5 B and  5 C  illustrate example graphs having different values for indicators of a connectivity metric, according to an embodiment of the present invention. 
         FIG.  6    illustrates an example reinforcement learning system, according to an embodiment of the present invention. 
         FIG.  7    illustrates an example tree search operation, according to an embodiment of the present invention. 
         FIG.  8    illustrates an example tree search operation in greater detail, according to an embodiment of the present invention. 
         FIG.  9    illustrates an apparatus provided in accordance with an embodiment of the present invention. 
         FIG.  10    illustrates an apparatus provided in accordance with another embodiment of the present invention. 
     
    
    
     It will be noted that throughout the appended drawings, like features are identified by like reference numerals. 
     DETAILED DESCRIPTION 
     As used herein, the term “about” should be read as including variation from the nominal value, for example, a +/−10% variation from the nominal value. It is to be understood that such a variation is always included in a given value provided herein, whether or not it is specifically referred to. 
     A satellite is likely to have different failure modes. The term “link equipment” is used herein to designate the equipment needed to operate an inter-satellite link in each satellite. Each piece of link equipment on a satellite may be designed as an independent module, so that the satellite can continue functioning after one or more link equipment failures. In this case, pieces of link equipment can potentially be repurposed as desired to support different communication links involving the satellite. Link equipment can similarly be used in other times of network devices which potentially for multiple communication links with other devices. A satellite can include multiple instances of link equipment, in order to concurrently support different links. Link equipment can be configured to implement a directional communication link, such as an optical or radio link. 
       FIG.  1    illustrates an example system involving a satellite network  102  and an apparatus for configuring same. The satellite network  102  is managed by a centralized OAM (operations, administration and maintenance) system  104 . The OAM system  102  may communicate with the satellite network  102  through a ground station  106 . When failures occur in the satellite network, they are reported back to the OAM system  104 . The OAM system  104  determines a reconfiguration of the satellite network in view of such failures, and implements the reconfiguration, for example by transmitting instructions, to other devices such as satellite devices, for implementing the reconfiguration. 
       FIGS.  2 A and  2 B  depict network nodes arranged in a geometrically regular mesh configuration. Such a configuration is anticipated in satellite networks, as the satellites&#39; orbital positions in a constellation typically must be precisely defined. As noted above, hard failures are difficult and expensive to repair in a satellite network, for example from an orbital repair platform. For example, a problematic satellite would need to be captured and possibly returned to the ground for corrective action. It is also likely that the satellite would need to be replaced. Due to the cost and time required for such maintenance, it is probable that hard failures would accumulate in the network and satellite nodes thereof until action is required. 
     As an alternative, and in accordance with some embodiments of the present invention, satellite resources can be repurposed improve the network performance in situ. This may be accomplished by repurposing connections such as inter-satellite links (ISLs). In  FIGS.  2 A and  2 B , the dashed lines  202  represent ISLs that have been repurposed in order to improve the overall network performance. In more detail, each satellite, represented by a circle  204  has four instances of link equipment (such as directional transceivers), represented by smaller squares  206 . In  FIG.  2 A , the links  202  have failed because of failures of the link equipment instances  206   a  and  206   b . In order to repurpose the satellite resources (link equipment) the two satellite nodes  204   a  and  204   b , holding the failed link equipment instances  206   a  and  206   b , respectively, are physically reoriented (e.g. rotated) so that the failed link equipment instances align, as shown in  FIG.  2 B . The number of broken links is reduced from two to one, thereby improving network connectivity. 
     In some embodiments configuring the network includes physically reorienting one, some or all network nodes, in order to reorient one of more directional transceivers thereof, for example as shown in  FIG.  2 B . The reorienting of directional transceivers affects one or more of the links between nodes. Therefore, in various embodiments configuring the entire network includes configuring one or more of the individual nodes. 
     Accordingly, in view of  FIGS.  2 A and  2 B , satellite nodes can be physically reoriented in order to reorient one or more link equipment instances (directional transceivers). This reorienting affects one or more links between nodes. 
     In order to effectively reconfigure the satellite network, embodiments of the present invention provide a means to evaluate multiple potential network configurations. As such, different potential configurations can be compared and evaluated. Embodiments of the present invention use “connectivity metrics” to evaluate the network configuration. This facilitates reconfiguring of the network from a state corresponding to a poorer connectivity metric, to a state corresponding to a better connectivity metric, for example after a failure event occurs. 
     Embodiments of the present invention combine particular connectivity metrics with one or more search methods for determining potential network configurations having desirable connectivity. The search methods use the connectivity metrics for evaluating potential network configurations. Embodiments of the present invention are applied in the context of a satellite OAM system. 
       FIG.  3    illustrates an example method  300  for configuring a communication network. The method includes, at step  302 , obtaining information indicative of current status of nodes of the communication network, links between the nodes of the communication network or a combination both nodes and links. The method further includes, at step  304 , processing the information to determine a potential new network configuration based on the obtained information. The potential new network configuration is implementable by adjusting one or more of the nodes, one or more of the links between network nodes (where appropriate), or a combination thereof. The processing includes evaluating at least the network configuration based on a connectivity metric indicative of an extent to which the nodes are interconnected via the links. The method further includes, at step  306 , providing instructions directing one or more underlying resources to implement the network configuration. The underlying resources can be network nodes themselves, or components of network nodes, or other equipment usable to perform network node adjustments or network configuration operations in general, whether physical, electrical or otherwise. In the case of  FIGS.  2 A and  2 B , the underlying resources can be physical actuators (e.g. thrusters such as propellant rockets) which are capable of rotating the satellite nodes. The instructions can cause network nodes to physically reconfigure in order to implement the network configuration. The instructions can cause network nodes to adjust operations, such as communication operations, in a manner that implements the network configuration. For example, the adjusting in operations can involve adjusting which communication equipment is used to support a given link, or which communication channel or frequency is used, or which of a plurality of communication modes (e.g. radio or optical) is used, or the like. The adjustment can depend on what options are available at a node for changing aspects that can affect its operations. 
     In some embodiments processing the information to determine the network configuration to be implemented includes evaluating one or more candidate network configurations based on the connectivity metric, and selecting the network configuration to be implemented as one of the candidate network configurations having at least a sufficient amount of connectivity based on the connectivity metric. In some embodiments, the candidate having the highest amount of network connectivity (among some or all candidates), or substantially the highest amount of network connectivity, can be selected. According to various embodiments, the connectivity metric is indicative of a network connectivity, which is generally an extent to which network nodes (e.g. satellite nodes) are interconnected via communication links, such as inter-satellite links. The links can be optical links for example involving communication lasers. The links can be wireless links for example at radio frequency, which can include microwave frequencies. 
     In various embodiments the current status of nodes in indicative of whether or not one or more of the nodes, or one or more of the links between nodes, is in an outage state. For greater clarity, an example of a link being in an outage state may include where one, or both, directional transceivers or link equipment instances has failed. As a result, these failed directional transceivers or link equipment may not allow a network node to communicate with either other network nodes or, for example, a ground station. An outage state could either be temporary or permanent, based on the reason for the transceiver or link equipment failure. For example, a temporary outage state could be caused by debris that has impaired the ability to communicate with other network nodes, while a permanent outage state could be caused by damaged link equipment. 
     In various embodiments the network includes a low-earth orbit (LEO) satellite constellation, or a plurality of LEO satellite constellations. Such a plurality of constellations may involve, for example, multiple trains of LEO satellites, where each train includes multiple satellites being spaced apart and following a same or similar orbital trajectory at a same or similar altitude. 
     In various embodiments the network includes a hybrid satellite constellation of LEO satellites and medium earth orbit (MEO) satellites. This may involve, for example, multiple trains of LEO satellites, where certain trains may be in communication with specific MEO satellites at different stages of an orbit. 
     In various embodiments the network includes a hybrid satellite constellation of LEO satellites and geostationary earth orbit (GEO) satellites. This may involve, for example, multiple trains of LEO satellites, where certain trains may be in communication with specific GEO satellites at different stages of an orbit. 
       FIG.  4    depicts a network configuration apparatus provided in accordance with an embodiment of the present invention. As illustrated, there are three connected elements: a metric  402 , an optimizer  404  and an accelerator  406 . The metric  402  quantifies the network design and may include metrics such as the connectivity metric  408 . The optimizer  404  determines desirable network configurations by evaluating candidate configurations using the connectivity metric  402 . The optimizer  404  may employ one or more of a variety of approaches such as but not necessarily limited to a tree search  412 , an optimization program (also referred to as a solver)  414  or a reinforcement learning system  416 . The optimization program or solver can be a computing system configured to perform computations in a predetermined manner in order to optimize or approximately determine a solution to a specified problem. For example, the optimization program or solver can determine a network configuration which maximizes or substantially maximizes an objective function, subject to constraints. The accelerator  406  improves the optimizer search time. This may be accomplished by using approaches such as a neural network  418 . For example, an optimizer performing a tree search  412  may use a neural network  418  to guide the search, such that for a given state, the neural network  418  would recommend a limited set of actions to explore, relative to all actions available to the tree search. 
     Different systems may make use of the connectivity metric to respond to changes in network configuration. For example, the connectivity metric may be used as the objective function of an optimization program, or alternatively as a constraint function. However, this use may be problematic as the connectivity metrics typically do not have the properties of linearity or convexity, and thus cannot easily be handled by some conventional optimization programs such as linear programming solvers. Alternatively, the connectivity metric may be used as the reward function for a reinforcement learning system, such as a Q-learning system. In various other systems, the connectivity metric may be used to assign node values to a tree search. 
     Various different connectivity metrics can be employed which provide a numerical (e.g. scalar or vector) value indicative of the network connectivity. In various embodiments, a graph theoretic approach is used to compute the connectivity metric. In such an approach, a representative matrix A consisting of numerical entries a ij , where i, j are row and column indices of the matrix, respectively, can be used to represent the network. Each entry a ij  represents the connectivity between two nodes i and j. For each i≠j, a ij  can be set to zero when a direct link between two nodes, labelled i and j, is absent. For i≠j, a ij  can be set to a nonzero value (e.g. one) when a direct link between two nodes, labelled i and j, is present. The diagonal values (i=j) can be set in a variety of ways. For example the diagonal values can be set to zero for an adjacency matrix, or to nonzero values as prescribed below for a Laplacian matrix. 
     The representative matrix A described above can be the Laplacian matrix. The Laplacian matrix has numerical matrix entries indicative of the existence of connectivity between nodes in one of the candidate configurations, and the numbers of links connecting to nodes in one of the candidate configurations. In some embodiments, the representative matrix A can be another matrix such as an adjacency matrix in which elements of the matrix indicate whether pairs of vertices are adjacent or not in a graph. The adjacency matrix is the same as the Laplacian, except that the diagonal elements are all zero. In various alternative embodiments, the diagonal elements can be equal to an arbitrary value (1 or 2) where there is a loop from a node to itself. 
     In various embodiments the connectivity metric is based at least in part on one or more eigenvalues of the network&#39;s representative (e.g. Laplacian) matrix. The network&#39;s representative matrix is indicative of one of the candidate network configurations. In various embodiments, evaluating candidate configurations includes computing some or all of the eigenvalues of the network&#39;s representative matrix. In some embodiments the connectivity metric is based at least in part on two or more eigenvalues of the network&#39;s representative matrix. Alternatively, the connectivity metric is based at least in part on all eigenvalues of the network&#39;s representative matrix. In some embodiments the two or more eigenvalues of the network&#39;s representative matrix, or all eigenvalues of the network&#39;s representative matrix, are expressed as a vector value or as a scalar value encoding multiple eigenvalues. 
     In various embodiments, the connectivity metric in use can be determined using spectral graph theoretic techniques, applied to a matrix such as the Laplacian or adjacency matrix. A graph spectrum is defined as the (potentially sorted) set of eigenvalues of the graph&#39;s representative (e.g. Laplacian) matrix. The eigenvalues can be sorted in order of size, e.g. in ascending or descending order. 
     Various techniques may be used to determine connectivity metrics. A non-limiting list of such techniques is discussed below. Embodiments of the present invention include determining the connectivity metrics using computation for example by an electronic device. 
     In various embodiments, the connectivity metric is indicative of the minimum number of elements (e.g. links between nodes) which would need to be removed in order to separate the network into two or more isolated portions. It is noted that the Cheeger number of a graph may be indicative of such a connectivity metric, where the Cheeger number of an undirected finite graph G is defined as: 
                 h   ⁡   (   G   )     =     min   ⁢     {               ❘   &#34;\[LeftBracketingBar]&#34;       ∂   A       ❘   &#34;\[RightBracketingBar]&#34;           ❘   &#34;\[LeftBracketingBar]&#34;     A     ❘   &#34;\[RightBracketingBar]&#34;         :   A     ⊆     V   ⁡   (   G   )       ,     0   &lt;       ❘   &#34;\[LeftBracketingBar]&#34;     A     ❘   &#34;\[RightBracketingBar]&#34;       ≤       1   2     ⁢       ❘   &#34;\[LeftBracketingBar]&#34;       V   ⁡   (   G   )       ❘   &#34;\[RightBracketingBar]&#34;             }         ,         
where V(G) is the vertex set of G, A denotes a subset of vertices V, and ∂A is the collection of all edges going from a vertex in A to a vertex outside of A. From the equation it is important to note that A does not contain more than half of the nodes in V. ∂A is the set of links connecting A with its complement.
 
     In various embodiments, the connectivity may be an algebraic connectivity, also known as Fiedler value, of a graph G. The algebraic connectivity is the second smallest eigenvalue of the Laplacian matrix of G. In some embodiments the connectivity metric is based at least in part on this second smallest eigenvalue of the Laplacian matrix. The algebraic connectivity is unique in that it has a mathematical relationship with the Cheeger number. 
     Similarly, the strength of a graph, which corresponds to the minimum ratio of edges removed to components created in a decomposition of the graph, may be used as the connectivity metric. The strength of a graph can be used to compute partitions of the set of vertices and detect zones of high concentration of edges. The strength of a graph is analogous to the toughness of a graph which, instead of the edges of a graph, focuses on the removal of vertices of a graph. 
     The cluster count of a graph is the number of disconnected partitions of the network. Similarly, network connectivity is defined as the number of edges that must be removed to partition the network. Either of these metrics may also be used as the connectivity metric. 
     In various embodiments, the connectivity metric is indicative of the numbers of links between network nodes. The connectivity metric can reflect one, some, or all of: the average (e.g. mean, median, mode, etc.) number of links between nodes, the minimum number of links between nodes, the maximum number of links between nodes, the distribution (e.g. via histogram) of numbers of links between nodes, the variance or standard deviation of numbers of links between nodes, or other statistical metrics. 
     In various embodiments, the connectivity metric is indicative of where network connections may be clustered together or, conversely, where parts of a network may only be weakly connected to other parts of the network. Similarly, the connectivity metric may indicate how many connections may need to be disconnected to partition or enlarge a network. 
       FIGS.  5 A,  5 B and  5 C  illustrate examples of how the connectivity metric may be indicative of the number of links between nodes and where those are links are located. In  FIG.  5 A , there is 1 cluster, the connectivity is 2, the Cheeger number is 0.5, the algebraic connectivity is 0.586, and the spectrum (sorted list of eigenvalues) is [0.0, 0.586, 1.0, 1.586, 2.0 . . . ]. In  FIG.  5 B , the connection between nodes ‘a’ and ‘b’ is removed, resulting in there being 1 cluster, the connectivity reducing to 1, the Cheeger number remaining 0.5, the algebraic connectivity reducing to 0.538, and the spectrum becoming [0.0, 0.538, 0.586, 1.29, 2.0 . . . ]. In  FIG.  5 C , connections between nodes ‘d’ and e′, and ‘g’ and ‘h’ are further removed resulting in there still being a single cluster, the connectivity remaining at 1, the Cheeger number reducing to 0.25, the algebraic connectivity further reducing to 0.132, and the spectrum becoming [0.0, 0.132, 0.586, 1.04, 2.0 . . . ]. 
     In various embodiments, the connectivity metric is selected based on a combination of usefulness and computability. Some connectivity metrics can be readily computed using spectral graph theory or other techniques, for example. Some of these metrics are more useful, in the sense that they readily identify network configurations that are operationally useful. For example, some connectivity metrics return generally higher values for networks which are substantially fully connected and robust to further failures. Embodiments of the present invention provide for certain general and specific forms of such connectivity metrics. A connectivity metric can be selected during system design, or the system can be configured to implement one of a plurality of connectivity metrics, which is either manually or automatically selectable. 
     In various embodiments, the reconfiguration of a satellite network (e.g. represented as a graph for evaluation purposes) is carried out via reinforcement learning and using algebraic connectivity as a metric. In further embodiments, this is accomplished using the Laplacian of a graph. The Laplacian of a graph is usually defined as the matrix L=D−A, where D is degree matrix of the graph and A is the adjacency matrix of the graph. The degree matrix is a diagonal matrix having off-diagonal entries equal to zero, and having each i th  diagonal entry d ii  entry equal to the number of edges (network links) attached to network node i, also referred to as vertex v i . The elements of L may this be written as: 
     
       
         
           
             
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     In some embodiments, the Laplacian will be scaled, for example having entries: 
     
       
         
           
             
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     This scaled variant may be used to relate graph spectra to the Cheeger constant. 
     Once the Laplacian is determined, the eigenvalues of the Laplacian may be computed and sorted. Various appropriate computing and sorting algorithms can be used, as would be readily understood by a worker skilled in the art. The computations may be approximate, or as exact as possible. 
       FIG.  6    depicts an example schematic of a reinforcement learning system which can be used according to embodiments of the present invention. A reinforcement learning system includes an agent  602  and the environment  604 . The environment  604  has a state  608  and a set of actions which act to change the state. The environment  604  also provides the agent  602  with a reward  606 . The reward  606  can be assigned based on the state  608  of the environment  604  or based on the state  608  of the environment  604  combined with an action (usually known as Q learning). The agent  602  interacts with the environment  604  to maximize the sequence of rewards  606  it receives. 
     The environment  604  may compute the algebraic connectivity of its current state  608  (or of some future state  608  after taking an action) and then send it to the agent  602  as a reward  606 . The agent  602  uses this reward  606  to learn which actions work well in different states in order to reconfigure the system after failures. 
     The agent  602  may be trained offline using a simulator that reproduces the network behavior. Alternatively, the agent  602  may be trained online, however as many thousands of scenarios are required for training, the network being managed may be in disarray until the agent  602  has learned how to effectively reconfigure the network. 
     Advantages of the above system include that it will learn how to reconfigure the network. The reinforcement learning system should be able to learn how to quickly reconfigure the network without expensive combinatorial searches. 
     The (e.g. ordered) set of eigenvalues of the graph&#39;s Laplacian are collectively known as the spectrum of the graph. In order to compare two or more spectra, the spectra must be sorted in ascending order. The spectra can then be compared lexicographically (i.e., item by item) to determine which spectrum is larger, smaller, or otherwise represents a more desirable network configuration. 
     Alternatively, a spectrum may be condensed into a single scalar value. The maximum possible value of any of the eigenvalues (which may be computed using the trace of the Laplacian or using other methods) can be designated as ‘k’. The metric may then be written as: M=k n-1 λ 0 +k n-2 λ 1 +k n-3 λ 2 + . . . λ n-1 . As with algebraic connectivity, larger values are better than smaller values. 
     In a preferred embodiment, the graph spectrum can be used with a tree search to determine the best action to take to improve the network configuration.  FIG.  7    depicts an example schematic of the tree search. Each node in the tree represents a state of the network. The root  702  of the tree is the current network state. Candidate actions create new states which are added to the tree as children of the current node. The search takes place recursively, starting with the root  702  node. As the recursion unwinds, each node tracks the best metric of all its children and which action is taken to reach that child. This mechanism allows each node to store the best action to take. 
     Thus, processing the information to determine the network configuration may include evaluating a plurality of candidate network configurations based on the connectivity metric using a tree search, and selecting the network configuration and one of the candidate network configurations evaluated using the tree search and having at least a sufficient amount of connectivity based on the connectivity metric. The tree search is performed on a tree having a root node, a plurality of branch nodes and a plurality of leaf nodes, each branch node and leaf node representing one of the candidate network configurations, and adjacent pairs of the branch nodes and leaf nodes representing candidate network configuration which differ by an incremental amount. 
     In some embodiments the tree search is a depth-first tree search. The tree search may be limited in depth. This may be necessary for performance reasons, as the search tree grows rapidly with increasing depth. 
     Alternatively, the search tree may use a neural network to guide the search. For a given state, the neural network would recommend a small set of actions to explore. The neural network may thus operate as an accelerator which is used in conjunction with the tree search to determine a network configuration to implement. 
     The system may use the results of the tree search in different ways. One step is to run a tree search. After the tree search is performed, the first action may be executed from the root. This would mean that a network reconfiguration corresponding to the first action from the root node would be performed. For example, the first action may be to reorient a particular network node. Once the first action is performed, then a new tree search may be run and the process described above may be repeated. These iterations would eventually stop, for example when the tree search cannot find an action to improve the network. 
     Another approach to using the results may be to run a tree search, after which a plurality of possible actions is executed. These actions may start from the root and proceed down to a particular leaf node. In this manner, multiple actions may be performed by a single running of the tree search. Referring to  FIG.  7   , actions may start at the root node  702  and then work their way down the branches, completing each action along the way. When all of the actions in a particular path from root to leaf node have been executed, a new tree search may be run and the process repeated. This method uses the same stopping criteria. 
     In various embodiments, tree search operations can be adjusted to avoid cycles. A cycle is where the system returns to a state it has previously been in during the same reconfiguration. It may be dangerous for a system to fall into a cycle as it may not be able to escape it. Therefore, a cycle would prevent a system from reconfiguring itself in a meaningful manner. To avoid cycles of this type, the tree search may be configured to remember the states it has already visited during the reconfiguration. These states may be viewed as constraints. These constraints may be treated as actions that are not included in the tree search because they would return the network to one of these cyclic states. 
     In some embodiments, the following heuristic can be implemented to improve search time. A boundary can be drawn around one or more anomalies (i.e. failed links) in the graph representation of the network. The search omits any actions that affect nodes outside of this boundary as they cannot improve the network configuration. This may be particularly important in situations where the network is being reconfigured in response to a failure, such as a link failure. This technique may provide a localized remedy for nodes that require reconfiguration, while allowing the nodes outside of the boundary to remain undisturbed. 
     In various embodiments processing the information to determine the network configuration may include training a machine learning agent to select, from among candidate network configuration, an adequately connected network configuration. The training includes providing feedback to the machine learning agent. The feedback is based at least in part on the connectivity metric. The training further includes operating the machine learning agent to select the network configuration based on the information indicative of the current status of nodes of the communication network, the links between the nodes of the communication network, or a combination thereof. In some embodiments the machine learning agent may use a neural network (e.g. as an accelerator) to evaluate a state-action-value function indicative of feedback to the machine learning agent. A state-action-value function, also called a Q function, specifies how good it is for a machine learning agent to perform a particular action in a state. Therefore, the feedback from the state-action-value function may be used to determine whether the machine learning agent should take a particular action. 
       FIG.  8    illustrates an example tree search operation in greater detail. Tree nodes are presented in boxes. Each tree node has specific attributes including Action (the action taken to get to that node from the parent node), BestChild (the child node of that node that has the best Value), Metric (the connectivity metric for the state that that particular node represents) and Value (the best metric taken from all the child nodes and this node). It should be noted that if all of the child nodes have a worse metric, then Metric and Value will be equal for a node. The connectivity metric in the present case is a list of eigenvalues arranged in ascending order. 
     Operation of the tree search may proceed as follows. At step  802 , a root node is created. At step  804 , the first child node is created at level 1. The action to get to Node 0 is to disconnect the link between network node 0-0 and network node 0-1. At step  806 , the first child node is created at level 2. The action to get here is to disconnect the link between network node 0-0 and network node 1-0. At step  808 , the first child node is created at level 3. To get to this state, disconnect the link between network node 0-1 and network node 0-2. 
     At step  810 , the tree search is limited to depth 3, so Node 0-0-0 does not create any children. The search then moves back to Node 0-0. The Value of Node 0-0-0 is worse than the Value of Node 0-0, so Node 0-0-0 is not marked as the best child of Node 0-0. At step  812 , Node 0-0-1 is created to explore the next action from Node 0-0. At step  814 , the tree search is limited to depth 3, so Node 0-0-1 does not create any children. The search returns to Node 0-0, and this time, the Value of Node 0-0-1 is better than the Value of Node 0-0, resulting in Node 0-0-1 being marked as the BestChild of Node 0-0. The Value of Node 0-0 is also updated to match the Value of Node 0-0-1. The search proceeds recursively in this manner, first exploring all the children of Node 0-0, then returning to Node 0 and exploring its children. A search tree such as this may have approximately 5000 nodes in it once the search is complete. At step  816 , once the tree search is completed, the best actions to take may be obtained by following the BestChild links. In the example of  FIG.  8   , the best child of the root node is Node 15. It should be noted that most nodes in this search have been omitted for brevity. The best child of Node 15 is Node 15-4, and since Node 15-4 does not have a best child, the two actions to be taken are: 1. Connect 1-1 to 1-2, and Connect 1-1 to 2-1. After one or more of the actions have been executed, the tree search may be repeated for a new network configuration. When the root node does not have a best child, the network configuration if final as the tree search cannot find any improvements to be made. 
       FIG.  9    illustrates an apparatus  900  located in a network node  910 , according to an embodiment of the present invention. The apparatus  900  includes a network interface  920  and processing electronics  930 . The network interface  920  can be a single network interface or a combination of network interfaces (e.g. including a satellite-to-satellite communication interface and a satellite-to-ground communication interface). The processing electronics can include components such as computer processors, graphics processing units, memory, digital or analog circuits, or the like, or a combination thereof. The processing electronics  930  can, by executing program instructions stored in memory, be configured to implement several operations as described herein. The processing electronics may include the memory, or the memory may be separate (not shown). 
     Accordingly, the processing electronics can be configured to implement a current status determiner  940  which, when configured, obtains information indicative of current status of the nodes of the communication network, links between the nodes of the communication network, or a combination thereof. Information indicative of current status of nodes may be obtained via, for example, network interface  920 , originating from, for example, a ground station that may be monitoring a plurality of nodes. 
     The processing electronics can further be configured to process the obtained information to determine a network configuration based on the obtained information. The processing electronics can be configured to provide a network configuration determiner  950  which may be configured to find a desired new configuration by computing the obtained information. The network configuration determiner  950  may compute what manner of instructions may be needed in order to achieve the new configuration 
     The processing electronics can be configured to implement an underlying resource instructor  960  which is configured to provide instructions directing one or more underlying resources to implement the network configuration. The underlying resource instructor  960  may be configured to adjust one of more of the nodes, one or more of the links between nodes, or a combination thereof. The processing of the obtained information includes evaluating at least the network configuration based on a connectivity metric indicative of an extent to which the nodes are interconnected via the links. 
     The current status determiner  940 , the network configuration determiner  950 , and the underlying resource instructor  960  can be configured to reconfigure multiple nodes of the communication network, multiple links between the nodes of the communication network, or a combination thereof. 
     In terms of messaging, and in some but not necessarily all embodiments, the apparatus  900  can receive, transmit, or both receive and transmit, via the network interface, various messages  980 . The apparatus can also transmit trigger messages  985  to other nodes, for causing the other nodes in relation to a reconfiguration process. Trigger messages may thereby be used to reconfigure multiple nodes. The apparatus can also transmit and receive network function messages  990 , which are messages communicated in accordance with an operation of the network itself. The apparatus can also transmit node location advertisement messages (not shown) indicative of current or future node location. Advertisements of location can be used in support of determining locations of network nodes. 
       FIG.  10    is a schematic diagram of an electronic device  1000  that may perform any or all of operations of the above methods and features explicitly or implicitly described herein, according to different embodiments of the present invention. For example, a computer equipped with network function may be configured as electronic device  1000 . 
     As shown, the device includes a processor  1010 , such as a Central Processing Unit (CPU) or specialized processors such as a Graphics Processing Unit (GPU) or other such processor unit, memory  1020 , non-transitory mass storage  1030 , I/O interface  1040 , network interface  1050 , and a transceiver  1060 , all of which are communicatively coupled via bi-directional bus  1070 . According to certain embodiments, any or all of the depicted elements may be utilized, or only a subset of the elements. Further, the device  1000  may contain multiple instances of certain elements, such as multiple processors, memories, or transceivers. Also, elements of the hardware device may be directly coupled to other elements without the bi-directional bus. Additionally or alternatively to a processor and memory, other electronics, such as integrated circuits, may be employed for performing the required logical operations. 
     The memory  1020  may include any type of non-transitory memory such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), read-only memory (ROM), any combination of such, or the like. The mass storage element  1030  may include any type of non-transitory storage device, such as a solid state drive, hard disk drive, a magnetic disk drive, an optical disk drive, USB drive, or any computer program product configured to store data and machine executable program code. According to certain embodiments, the memory  1020  or mass storage  1030  may have recorded thereon statements and instructions executable by the processor  1010  for performing any of the aforementioned method operations described above. 
     It will be appreciated that, although specific embodiments of the technology have been described herein for purposes of illustration, various modifications may be made without departing from the scope of the technology. The specification and drawings are, accordingly, to be regarded simply as an illustration of the invention as defined by the appended claims, and are contemplated to cover any and all modifications, variations, combinations or equivalents that fall within the scope of the present invention. In particular, it is within the scope of the technology to provide a computer program product or program element, or a program storage or memory device such as a magnetic or optical wire, tape or disc, or the like, for storing signals readable by a machine, for controlling the operation of a computer according to the method of the technology and/or to structure some or all of its components in accordance with the system of the technology. 
     Acts associated with the method described herein can be implemented as coded instructions in a computer program product. In other words, the computer program product is a computer-readable medium upon which software code is recorded to execute the method when the computer program product is loaded into memory and executed on the microprocessor of the wireless communication device. 
     Further, each operation of the method may be executed on any computing device, such as a personal computer, server, PDA, or the like and pursuant to one or more, or a part of one or more, program elements, modules or objects generated from any programming language, such as C++, Java, or the like. In addition, each operation, or a file or object or the like implementing each said operation, may be executed by special purpose hardware or a circuit module designed for that purpose. 
     Through the descriptions of the preceding embodiments, the present invention may be implemented by using hardware only or by using software and a necessary universal hardware platform. Based on such understandings, the technical solution of the present invention may be embodied in the form of a software product. The software product may be stored in a non-volatile or non-transitory storage medium, which can be a compact disk read-only memory (CD-ROM), USB flash disk, or a removable hard disk. The software product includes a number of instructions that enable a computer device (personal computer, server, or network device) to execute the methods provided in the embodiments of the present invention. For example, such an execution may correspond to a simulation of the logical operations as described herein. The software product may additionally or alternatively include number of instructions that enable a computer device to execute operations for configuring or programming a digital logic apparatus in accordance with embodiments of the present invention. 
     Although the present invention has been described with reference to specific features and embodiments thereof, it is evident that various modifications and combinations can be made thereto without departing from the invention. The specification and drawings are, accordingly, to be regarded simply as an illustration of the invention as defined by the appended claims, and are contemplated to cover any and all modifications, variations, combinations or equivalents that fall within the scope of the present invention.