Effective Approaches for Constructing Fault-Tolerant Communication Trees in Hypercubes

Abstract

A communication tree is a binomial tree embedded in a hypercube, whose communication direction is from the leaves to the root. If a problem to be solved can be divided into independent subproblems, each subproblem can first be solved by one of the hypercube processors and all subresults can then be merged into the final results through tree communication. For this purpose, we propose using two random search techniques, the genetic algorithm (GA) and the simulated annealing (SA) approaches, to construct fault-tolerant communication trees with the lowest data transmission time. Experimental evaluation shows that with reasonably low search time, our proposed GA and SA approaches are able to find more desirable communication trees (i.e., trees with less data transmission time) than the minimal cost approach. We also introduce a distributed approach which, under the aid of two algorithms, is able to effectively reduce search time for the GA and SA approaches due to parallel search for communication subtrees in disjoint subcubes.