On the Optimum Communication Cost Problem in Interconnection Networks: Finding Near-Optimum Solutions for Topology Design Problems Using Randomized Algorithms

In the Optimum Communication Spanning Tree (OCST) problem, a spanning tree for a complete graph has to be found that satisfies the communication requirements needed by the vertices with a minimum total cost. A special case of the OCST problem is the Optimum Distance Spanning Tree (ODST) problem, where the requirements are restricted to be constant. Both problems are known to be NP-hard. In this book, a randomized algorithm has been proposed to efficiently solve two special cases of the ODST problem. This can be achieved by randomly generating spanning trees with certain properties. This book also includes the history of the OCST problem along with a literature survey. This is in addition to a discussion on the different deterministic algorithms that exist for enumerating all spanning trees of a graph. An empirical study has been conducted that showed that the proposed algorithm can yield near- optimum solutions. The experiments involve testing the proposed algorithm to solve these special cases using several randomly generated graphs, in addition to the hypercube and butterfly network topologies to some specified dimension.