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Optimal total exchange in Cayley graphs

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2 Author(s)
Dimakopoulos, V.V. ; Dept. of Comput. Sci., Ioannina Univ., Greece ; Dimopoulos, N.J.

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 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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Parallel and Distributed Systems, IEEE Transactions on  (Volume:12 ,  Issue: 11 )