On the Optimum Communication Cost Problem in Interconnection Networks

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.