Distributed memorization for the k-vertex cover problem

  • Authors:

  • Peter J. Taillon

  • Affiliations:

  • School of Computer Science, Carleton University, Ottawa, Ontario, Canada

  • Venue:
  • ISPA'07 Proceedings of the 5th international conference on Parallel and Distributed Processing and Applications
  • Year:
  • 2007

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Abstract

We present the first investigation of the well-known memorization technique for solving the k-Vertex Cover problem in a distributed setting. Memorization was introduced by Robson [15] in his paper on solving the Maximum Independent Set problem. The idea is to augment a recursive algorithm with the capability to store subproblem instances and solutions of bounded size in a table that can be quickly referenced, so that subproblems are guaranteed to be solved exactly once. This approach has recently been applied with success to improve the complexity of the fixed-parameter tractable algorithms for solving the k-Vertex Cover problem [12,5]. We present a general parallel approach for using memorization to solve the k-Vertex Cover problem where the subgraphs are precomputed [12]. In this case, the subgraphs and corresponding solutions are generated in a preprocessing step, rather than during the recursion. Our technique makes efficient use of the processors generating the lookup table, while at the same time requiring less space. We describe a distributed algorithm using this technique, well-suited to cluster or grid computing platforms.