Article ID Journal Published Year Pages File Type
435571 Theoretical Computer Science 2016 10 Pages PDF
Abstract

All-to-all communication occurs in many important applications in parallel processing. In this paper, we study the all-to-all broadcast number (the shortest time needed to complete the all-to-all broadcast) of Cartesian product of graphs under the assumption that: each vertex can use all of its links at the same time, and each communication link is half duplex and can carry only one message at a unit of time. We give upper and lower bounds for the all-to-all broadcast number of Cartesian product of graphs and give formulas for the all-to-all broadcast numbers of some classes of graphs, such as the Cartesian product of two cycles, the Cartesian product of a cycle with a complete graph of odd order, the Cartesian product of two complete graphs of odd order, and the hypercube Q2nQ2n under this model.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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