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<p><b>Abstract</b>—Consider an interconnection network and the following situation: Every node needs to send a different message to every other node. This is the <it>total exchange</it> or <it>all-to-all personalized communication</it> 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 (<it>single-port</it> 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 <it>any</it> 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 <it>node-invariant</it> algorithms and which behave uniformly across the network.</p>
Cayley graphs, collective communications, interconnection networks, node-invariant algorithms, total exchange (all-to-all personalized communication).

V. V. Dimakopoulos and N. J. Dimopoulos, "Optimal Total Exchange in Cayley Graphs," in IEEE Transactions on Parallel & Distributed Systems, vol. 12, no. , pp. 1162-1168, 2001.
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