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Optimal Total Exchange in Cayley Graphs
November 2001 (vol. 12 no. 11)
pp. 1162-1168

Abstract—Consider an interconnection network and the following situation: Every node needs to send a different message to every other node. This is the total exchange or all-to-all personalized communication problem, one of a number of information dissemination problems known as collective communications. Under the assumption that a node can send and receive only one message at each step (single-port model), it is seen that the minimum time required to solve the problem is governed by the status (or total distance) of the nodes in the network. We present here a time-optimal solution for any Cayley network. Rings, hypercubes, cube-connected cycles, and butterflies are some well-known Cayley networks which can take advantage of our method. The solution is based on a class of algorithms which we call node-invariant algorithms and which behave uniformly across the network.

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Index Terms:
Cayley graphs, collective communications, interconnection networks, node-invariant algorithms, total exchange (all-to-all personalized communication).
Vassilios V. Dimakopoulos, Nikitas J. Dimopoulos, "Optimal Total Exchange in Cayley Graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 11, pp. 1162-1168, Nov. 2001, doi:10.1109/71.969126
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