The complete exchange (or all-to-all personalized) communication pattern occurs frequently in many important parallel computing applications. We discuss several algorithms to perform complete exchange on a two dimensional mesh connected computer with wormhole routing. We propose algorithms for both powerof-two and non power-of-two meshes as well as an algorithm which works for any arbitrary mesh. We have developed analytical models to estimate the performance of the algorithms on the basis of

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... stem parameters. These models take into account the e ects of link contention and other characteristics of the communication system. Performance results on the Intel Touchstone Delta are presented and analyzed.