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<p>In multicomputers that utilize circuit switching or wormhole routing, communicationoverhead depends largely on link contention-the variation due to distance between nodesis negligible. This has a major impact on the load balancing problem. In this case there are some nodes with an excess load (sources) and other with a deficit load (sinks). Amatching of sources to sinks is required to avoid contention. The problem is madecomplex by the hardwired routing on currently available machines: The user can controlonly which nodes communicate but not how the messages are routed. Network flowmodels of message flow in the mesh and the hypercube have been developed to solvethis problem. The crucial property of these models is the correspondence betweenminimum cost flows and correctly routed messages. To solve a given load balancingproblem, a minimum cost flow algorithm is applied to the network. This permits theefficient determination of a maximum contention free matching of sources to sinks that, in turn, tells how much of the given imbalance can be eliminated without contention.</p>
Index Termsnetwork flow model; load balancing; circuit-switched multicomputers; wormhole routing;hypercube; minimum cost flow algorithm; contention free matching; concurrency control; hypercube networks; multiprocessing systems

S. Bokhari, "A Network Flow Model for Load Balancing in Circuit-Switched Multicomputers," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 649-657, 1993.
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