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A new methodology named CALMANT (CC-cube Algorithms on Meshes and Tori) for mapping a kind of algorithms that we call CC-cube algorithm onto multicomputers with hypercube, mesh, or torus interconnection topology is proposed. This methodology is suitable when the initial problem can be expressed as a set of processes that communicate through a hypercube topology (a CC-cube algorithm). There are many important algorithms that fit into the CC-cube type. CALMANT is based on three different techniques: a) the standard embedding to assign the processes of the algorithm to the nodes of the mesh multicomputer; b) the communication pipelining technique to increase the level of communication parallelism inherent in the CC-cube algorithms; and c) optimal message-scheduling algorithms proposed in this work in order to avoid conflicts and minimizing in this way the communication time. Although CALMANT is proposed for multicomputers with different interconnection network topologies, this paper only focuses on the particular case of meshes. [ABSTRACT FROM AUTHOR]