# Patent

## Title
Method and apparatus for interleaved exchange in a network mesh

## Abstract

A method for exchanging information within a mesh network that has an array of nodes defined by four quadrants. The method includes the initial step of exchanging information from a set of nodes in one quadrant to a set of nodes located in an adjacent quadrant. The exchange of information simultaneously occurs in both a vertical and horizontal direction within the array. Information is then exchanged between nodes within the same quadrant and subquadrants.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
This application is a divisional application of U.S. patent application No. 09/879,030 filed Jun. 12, 2001, now U.S. Pat. No. 6,460,128, which is a continuation of U.S. patent application Ser. No. 09/624,287 filed Jul. 24, 2000, now U.S. Pat. No. 6,356,992, which is a divisional application of U.S. patent application Ser. No. 08/773,262 filed Dec. 23, 1996, now U.S. Pat. No. 6,173,387, which is a continuation of U.S. patent application Ser. No. 08/571,694 filed Dec. 12, 1995, now abandoned, which is a continuation of U.S. patent application No. 08/241,182, filed May 11, 1994, now abandoned.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method of transmitting information within a network.
2. Description of Related Art
To increase the size, speed and scalability of computer systems, computers may be linked together within a network to process information in parallel. Such systems are commonly referred to as parallel processing networks. Parallel processing networks typically have a plurality of microprocessor based components coupled together by busses and associated hardware. Each processor based component functions as a node which can transmit information to other nodes within the network.
The nodes can be arranged as a plurality of interconnected cubes, commonly referred to as a hypercube. Hypercubes require a large number of data links, which increase the size of the system.
The nodes can also be arranged in a two-dimensional array, commonly referred to as a network mesh. FIGS. 1a-d show a method of exchanging information within a mesh that is commonly referred to as the Direct Exchange Algorithm. In the Direct Exchange method, information is exchanged from one node to another node within the same row of the mesh. The process is repeated until the information of one node is transferred to each of the nodes within the row. For example, as shown in FIG. 1a, in the first step, the information from node 1 is transferred to node 3, node 2 transfers information to node 1, node 3 transfers information to node 4 and the information of node 4 is transferred to node 2. The process of exchanging information between nodes is repeated in accordance with the patterns shown in FIGS. 1b, 1c and 1d. The information can then be exchanged between rows and the process is repeated. Although the Direct Exchange Algorithm has a relatively high transmission rate, the number of messages and the start-up time to send the messages from each node rapidly increases with the size of the mesh.
FIGS. 2a-f and 3a-d show other methods of exchanged information within a mesh, commonly referred to as the Binary Exchange Algorithm and the Quadrant Exchange Algorithm, respectively. Both of these methods utilize a store and forward approach, wherein each node can both receive and forward information transmitted by another node. As shown in FIG. 2a, in the first step of the Binary Exchange method, the nodes in one half of the mesh transmit information to nodes in the other half of the mesh in a horizontal direction. The process is repeated by sending the information from one half of the mesh to the other half of the mesh in a vertical direction, as shown in FIG. 2b. As shown in FIGS. 2c-f, the information is then exchanged within quadrants and subquadrants of the mesh.
In the Quadrant Exchange method, information is exchanged within rectangular groups of nodes as shown in FIGS. 3a and 3b. As shown in FIG. 3C, the information is then exchanged within separate quadrants of the mesh. Although both the Binary and Quadrant Exchange methods can be used in large mesh networks, the start-up time and transmission rate are relatively slow. Additionally, the Quadrant method is susceptible to node contention. It would be desirable to provide an algorithm for a mesh network, that was not susceptible to node contention and had a relatively high complete information exchange rate.
SUMMARY OF THE INVENTION
The present invention is a method for exchanging information within a mesh network that has an array of nodes defined by four quadrants. The method includes the initial steps of exchanging information from a set of nodes in one quadrant to a set of nodes located in an adjacent quadrant. The exchange of information simultaneously occurs in both a vertical and horizontal direction within the array. Information is then exchanged between nodes within the same quadrant and subquadrants.



BRIEF DESCRIPTION OF THE DRAWINGS
The objects and advantages of the present invention will become more readily apparent to those ordinarily skilled in the art after reviewing the following detailed description and accompanying drawings, wherein:
FIGS. 1a-d are schematics showing information being exchanged between nodes arranged in a row in accordance with a method in the prior art;
FIGS. 2a-f are schematics showing information being exchanged between nodes arranged in a two-dimensional array in accordance with a method in the prior art;
FIGS. 3a-c are schematics showing information being exchanged between nodes arranged in a two-dimensional array in accordance with a method in the prior art;
FIG. 4 is a schematic of a mesh network having an array of nodes that can transfer information;
FIG. 5 is a schematic showing a node exchanging data with four neighboring nodes;
FIG. 6a is a schematic of a four by four array of nodes showing a first step of the present method;
FIG. 6b is a schematic similar to FIG. 3a showing a second step of the method;
FIG. 6c is a schematic similar to FIG. 3a showing a third step of the method;
FIG. 6d is a schematic similar to FIG. 3a showing a fourth step of the method;
FIGS. 7a-h are schematics showing the method in an eight by eight array of nodes.



DETAILED DESCRIPTION OF THE INVENTION
The present invention is a method for exchanging information within a mesh network that has an array of nodes defined by four quadrants. The method includes the initial steps of exchanging information from a set of nodes in one quadrant to a set of nodes located in an adjacent quadrant. The exchange of information simultaneously occurs in both a vertical and horizontal direction within the array. Information is then exchanged between nodes within the same quadrant and subquadrants.
Referring to the drawings more particularly by reference numbers, FIG. 4 shows a mesh network which has a plurality of nodes labeled 1-16. Each node is capable of transmitting and receiving information from another node. As shown in FIG. 5, in the preferred embodiment, each node is a functional computer on a card 20 that can be plugged into the network. The card 20 contains a microprocessor, memory and other associated hardware required to process information. The computer cards 20 contain an interface 22 that couples the components of the card to a number of busses 24. The busses are connected to other cards (nodes) and provide a medium to exchange information between the cards. The cards typically process information in parallel, wherein the mesh is a parallel processing network.
Each card generates an address for the destination node, along with the information that is to be transmitted to the other node. The address and information are then sent to a node in accordance with the algorithm of the present invention. The transmitting node may also receive information from the destination node. The receiving node stores both the address and the information sent by the transmitting node. If the receiving node has a matching address (destination node) then the node processes the information. If the address of the receiving card does not match the destination address, then the card forwards the address and information to the next node, again in accordance with the algorithm of the present invention. In the preferred embodiment, each node transfers information to a receiving node through a dedicated bus, to avoid bus contention within the system.
The network has a controller 26 which controls the exchange of information between the nodes. The controller 26 controls which node will receive the information. For example, in accordance with the algorithm of the present invention, the card 20 at node 1 may initially exchange information with node 3, then exchange information with node 9 and finally exchange information with nodes 2 and 5. In the first step, the controller 26 enables the interface of the cards at nodes 1 and 3 to exchange information. The controller 26 may initially allow information generated by node 1 to be transmitted to node 3, and the information generated by node 3 to be subsequently transmitted to node 1. The controller can control the bus and corresponding node that is to receive the information by providing a command to the card or driving active one or more control signals that enable each bus.
If the information sent by node 3 is to be processed by node 1, the card at node 1 processes the information. If the information transmitted by node 3 is not to be processed by node 1, node 1 retransmits the information generated by node 3 to node 9 in accordance with the second step of the algorithm. Node 1 also receives information from node 9, and the process is repeated with nodes 2 and 5.
FIGS. 6a-6d show the steps of exchanging information within a 4 by 4 array of nodes in accordance with an algorithm of the present invention. The lines indicate the path of information exchanged between the corresponding nodes. The first step is shown in FIG. 6a, wherein nodes 1, 6, 9 and 14 exchange information with nodes 3, 8, 11 and 16, respectively, in a horizontal direction of the array, and nodes 2, 4, 5 and 7 exchange information with nodes 10, 12, 13 and 15, in a vertical direction of the array. The exchange of information is interleaved between the nodes, so that none of the nodes both receive and transmit information from more than one node. The interleaving pattern prevents node contention.
FIGS. 6a-6d show the steps of transferring information within a 4 by 4 array of nodes in accordance with an algorithm of the present invention. The lines indicate the path of information transferred between the corresponding nodes. The first step is shown in FIG. 6a, wherein nodes 1, 6, 9 and 14 transfer information with nodes 3, 8, 11 and 16, respectively, in a horizontal direction of the array, and nodes 2, 4, 5 and 7 transfer information with nodes 10, 12, 13 and 15, in a vertical direction of the array. The transfer of information is interleaved between the nodes, so that none of the nodes both receive and transmit information from more than one node. The interleaving pattern prevents node contention.
The second step of the algorithm is shown in FIG. 6b, wherein the nodes that exchanged information horizontally in the first step, exchange information vertically, and the nodes that exchanged information vertically exchange horizontally. Accordingly, in the second step, nodes 1, 3, 6 and 8 exchange information with nodes 9, 11, 14, and 16, respectively in the vertical direction, and nodes 2, 5, 10 and 13 exchange information with nodes 4, 7, 12 and 15, respectively in the horizontal direction.
FIGS. 6c and 6d, show steps three and four of the present algorithm, respectively, wherein the nodes exchange information within the same quadrant of the mesh. In step three (FIG. 6c) the nodes all exchange information horizontally with an adjacent node in the same quadrant. In step four (FIG. 6d) the nodes all exchange information vertically with an adjacent node in the same quadrant. The steps shown in FIGS. 6a-d are then repeated.
FIGS. 7a-h show the algorithm of the present invention being performed within an 8 by 8 array of nodes. Like the process of exchanging information in the 4 by 4 array, the nodes in one quadrant of the mesh exchange information to nodes in an adjacent quadrant of the array in both the vertical and horizontal directions. The process of exchanging information between quadrants of nodes is repeated three more times as shown in FIGS. 7b-d. The nodes then exchange information with nodes of the same quadrant and subquadrant as shown in FIGS. 7e-h. Although 4 by 4 and 8 by 8 nodal arrays are shown and described, it is to be understood that the algorithm of the present claimed invention can be used in other two-dimensional nodal arrays.
Latency (α): the latency is defined as the start up time required to exchange a message and includes fixed overheads associated with each message. α typically has the units of seconds.
Bandwidth (B): the bandwidth is the rate at which information can be transmitted along the communication links between the nodes. B typically has the units of bytes/sec.
Rearrangement rate (δ): the rearrangement rate is the rate at which information can be rearranged at the node for further transmission. δ typically has the units of bytes/sec.
The complete exchange of information using the algorithm of the present invention is defined by the following equation. 



  
    
      2
      K
    
    ⁢
    α
  
  +
  
    
      2
      
        (
        
          K
          -
          1
        
        )
      
    
    ⁢
    
       
    
    ⁢
    
      mn
      B
    
  
  +
  
    K
    ⁢
    
       
    
    ⁢
    
      mn
      δ
    
  




wherein;

    
    
        m=the bytes of data transferred.
        n=the number of nodes in the network.
        K=log2√{square root over (n)} {or k such that n=2k·2k}.

The first term of the equation relates to the latency of the system, the second term corresponds to the system bandwidth, and the last term defines the rearrangement rate. Table I shows the different terms of the equation for the method of the present invention (entitled Interleaved Binary Exchange) with similar terms for information exchange equations relating to the Direct Exchange algorithm, Binary Exchange algorithm and the Quadrant Exchange algorithm.

    
    













TABLE I








Transmission
Rearrangement



Start-Up Time
Time
Time




















Binary Exchange
Absolute Relative
2(2k − 1)α  ̃2




  
    (
    
      
        2
        k
      
      -
      1
    
    )
  
  ⁢
  
     
  
  ⁢
  
    nm
    β
  



  ̃2




  k
  ⁢
  
    nm
    δ
  



 1


Direct Exchange
Absolute Relative
2(3k − 2)α 22k/4




  
    
      2
      k
    
    4
  
  ·
  
    nm
    β
  



 1/2
None 0


Quadrant Exchange
Absolute Relative
3(2k − 1)α  ̃3




  
    3
    4
  
  ⁢
  
    (
    
      
        2
        k
      
      -
      1
    
    )
  
  ⁢
  
    nm
    β
  



  ̃3/2




  k
  ⁢
  
    mn
    δ
  



 1


Interleaved Binary Exchange
Absolute Relative
2kα 1




  
    1
    2
  
  ⁢
  
    (
    
      2
      k
    
    )
  
  ⁢
  
    mn
    β
  



 1




  k
  ⁢
  
    mn
    δ
  



 1









As shown in Table I, the algorithm of the present invention provides improved performance over both the Binary Exchange and Quadrant Exchange algorithms by reducing the start-up and transmission times. The Direct Exchange algorithm provides better performance for both the transmission time and the rearrangement time, but the start-up time and number of messages increases drastically for larger mesh networks. The present invention thus provides an algorithm that improves the performance of scalable parallel processing networks over algorithms in the prior art.
While certain exemplary embodiments have been described and shown in the accompanying drawings, it is to be understood that such embodiments are merely illustrative of and not restrictive on the broad invention, and that this invention not be limited to the specific constructions and arrangements shown and described, since various other modifications may occur to those ordinarily skilled in the art.

## Claims

1. A method in a mesh network to exchange data to perform parallel processing, the method comprising:
providing a plurality of computer cards each having an interface to transfer information as a processor node in the mesh network and arranged in a square two dimensional matrix of processor nodes in the mesh network; 
providing a plurality of dedicated busses coupled to the plurality of computer cards to interconnect the plurality of computer cards and to allow the exchange of data there between; 
associating each of the plurality of computer cards in the mesh network with an address; and 
each of the plurality of computer cards 
generating information to transfer to a destination processor node, 
generating an address for the destination processor node, and 
transferring the information and the address to another computer card in accordance with the node order specified by an interleaved binary exchange algorithm with a multi-stage information transfer cycle, in at least one stage of the information transfer cycle information is concurrently transferred in only a vertical direction between some processor nodes diagonally aligned in the mesh network and in only the horizontal direction between other processor nodes diagonally aligned in the mesh network.

2. The method of claim 1, wherein
the processor nodes associated with the plurality of computer cards are arranged into four non-overlapping quadrants and each quadrant is arranged into four non-overlapping subquadrants, and 
the interleave binary exchange algorithm is as shown in FIGS. 6a through 6d.

3. The method of claim 1, wherein
the processor nodes associated with the plurality of computer cards are arranged into four non-overlapping quadrants and each quadrant is arranged into four non-overlapping subquadrants, and 
the interleave binary exchange algorithm is as shown in FIGS. 7a through 7h.

4. The method of claim 1, wherein
each computer card includes, 
a processor to process data, 
a memory to store data, and 
a bus interface to couple the processor to one of the plurality of busses and to couple the memory to one of the plurality of busses.

5. The method of claim 1, wherein
each computer card 
receives generated information and address from another computer card as specified by the interleaved binary exchange algorithm, 
compares its address with the generated address to determine if the generated information should be processed by it, and 
transfers the generated address and the generated information to the next computer card as specified by the interleaved binary exchange algorithm.

6. The method of claim 5, wherein
the processor nodes associated with the plurality of computer cards are arranged into four non-overlapping quadrants and each quadrant is arranged into four non-overlapping subquadrants, and 
the interleave binary exchange algorithm is as shown in FIGS. 6a through 6d.

7. The method of claim 5, wherein
the processor nodes associated with the plurality of computer cards are arranged into four non-overlapping quadrants and each quadrant is arranged into four non-overlapping subquadrants, and 
the interleave binary exchange algorithm is as shown in FIGS. 7a through 7h.

8. A method comprising:
generating information by selected nodes of an array of nodes; and 
transferring the information in accordance with a node order specified by an interleaved binary exchange algorithm with a multi-stage information transfer cycle, the transferring of the information comprises 
transferring information in a vertical direction between a first group of nodes aligned diagonally along the array of nodes; 
transferring information in the horizontal direction between a second group of nodes aligned diagonally along the array of nodes differing from the first group of nodes, the transfer in the horizontal direction being concurrent with the transfer in the vertical direction, and 
the first group of nodes being adapted to intitially transfer information in only the vertical direction and the second group of nodes being adapted to initially transfer information in only the horizontal direction concurrently with the transfer of information in the vertical direction.

9. The method of claim 8, wherein prior to transferring information, including a destination address for the information, the method further comprising:
arranging the plurality of nodes that comprises computer cards into 2n non-overlapping quadrants and each quadrant being arranged into 2n non-overlapping subquadrants, where n≧m.

10. The method of claim 9, wherein n and m are equal to two.

11. The method of claim 8, wherein the first group of nodes represents one-half of the plurality of nodes.

12. The method of claim 8, wherein the second group of nodes represents the other half of the plurality of nodes.

13. The method of claim 8, wherein each of the plurality of nodes being a computer card that comprises (1) a processor, (2) a memory, and (3) a bus interface coupling the processor to one of a plurality of dedicated buses and coupling the memory to one of the plurality of dedicated buses.

14. The method of claim 8, wherein the transferring of information and the destination addresses further comprising:
transferring information and destination addresses in the horizontal direction between the first group of nodes; and 
transferring information and destination address in the vertical direction between the second group of nodes.

15. The method of claim 14 further comprising:
transferring information and destination addresses in the horizontal direction between nodes in the same subquadrant; and 
transferring information and destination addresses in the vertical direction between nodes in the same subquadrant.

16. A method comprising:
generating information by a first node of a plurality of nodes forming an array of nodes; and 
transferring the information in accordance with a node order specified by an interleaved binary exchange algorithm with a multi-shape information transfer cycle by 
transferring information in a vertical direction for a first group of nodes of the plurality of nodes diagonally aligned within the array of nodes, 
transferring information in the horizontal direction between a second group of nodes of the plurality of nodes diagonally aligned within the array of nodes concurrently with the transferring of information in the vertical direction, the second group of nodes being different from the first group of nodes, and 
the first group of nodes being adapted to initially transfer information in only the vertical direction and the second group of nodes being adapted to initially transfer information in only the horizontal direction concurrently with the transfer of information in the vertical direction.

17. The method of claim 16, wherein the information comprises a destination address for the information.

18. The method of claim 17, wherein each of the plurality of nodes is a computer card.

19. The method of claim 17, wherein prior to generating information by the first node, the method further comprising:
arranging the plurality of nodes into four overlapping quadrants, each quadrant being arranged into four non-overlapping subquadrants.

20. The method of claim 16, wherein the transferring of information in the vertical direction is conducted by a first half of the plurality of nodes.

21. The method of claim 20, wherein the tranferring of information in the horizontal direction is conducted by a second half of the plurality of nodes.

22. The method of claim 21, wherein the first half of the plurality of nodes having no common node with the second half of the plurality of nodes.

23. A method comprising:
generating information by a first node of a plurality of nodes of an array of nodes; 
transferring the information in accordance with a node order specified by an interleaved binary exchange algorithm with a multi-stage information transfer cycle by 
transferring information in a vertical direction a first group of nodes of the plurality of nodes formed diagonally using the array of nodes, and 
transferring information in the horizontal direction between a second group of nodes of the plurality of nodes diagonally along the array of nodes concurrently with the transferring of information in the vertical direction, the second group of nodes being different from the first group of nodes, 

the interleaved binary exchange algorithm defined by 

 2kα+2(k−1)(mn/B)+k(mn/δ)
 where: 
m=number of bytes of information; 
α=a latency, which is a start-up time required to exchange information; 
B=a bandwidth, which is a rate at which information can be transmitted along communication links, in bytes per second; and 
δ=a rearrangement rate, which is a rate at which information can be rearranged at a node for subsequent transmission, in bytes per second.