Communication heuristics in distributed combinatorial search algorithms

Abstract

Algorithms for combinatorial search problems such as the travelling salesman problem, the polynomial problem or game-tree searching have been prime candidates for a distributed implementation as these problems offer substantial parallelism on the programm level. However, a number of experimental studies show that naive approaches to distributed combinatorial search tend to yield only a moderate speedup. The problem is to find a communication strategy that is able to limit stand-stills and superfluous searching of individual processors by distributing the work-load and intermediate results among the processors effectively and that causes only moderate communication overhead. To tackle the problem of the diffusion of commonly useful intermediate results between processors linked by “slow” communication lines without shared memory, we propose a formal method to derive optimal and adaptive communication strategies based on Dynamic Programming in Markov Chains. The key idea of our approach is to compare the running time to be expected under the current contents of the local copy of the shared state with the search and communication effort when acquiring the intermediate result of another processor via an exchange of messages. Using this method we study communication strategies for various distributed combinatorial search problems: for the distributed determination of the maximum of a vector, for a distibuted version of a simple variant of alpha-beta pruning, and for distributed branch and bound methods, where we examine the set partitioning problem.