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Parallel Algorithms for Combinatorial Search Problems

Zhang, Yanjun
Technical Report Identifier: CSD-89-543
November 1989

Abstract: This thesis is a theoretical study of parallel algorithms for combinatorial search problems. In this thesis we present parallel algorithms for backtrack search, branch-and-bound computation and game-tree search.

Our model of parallel computation is a network of processors communicating via messages. Our primary interest in a parallel algorithm is its speed-up over the sequential ones. Our goal is to design parallel algorithms that achieve a speed-up proportional to the number of processors used.

We first study backtrack search that enumerates all solutions to a combinatorial problem. We propose a simple randomized method for parallelizing sequential backtrack search algorithms for solving enumeration problems. We show that, uniformly on all instances, this method is likely to achieve a nearly best possible speed-up.

We then study the branch-and-bound method for solving combinatorial optimization problems. We present a randomized method called Local Best-First Search for parallelizing sequential branch-and-bound algorithms. We show that, uniformly on all instances, the execution time of this method is unlikely to exceed a certain inherent lower bound by more than a constant factor.

In the rest of this thesis we study the problem of evaluation of game trees in parallel. We present a class of parallel algorithms that parallelize the "left-to-right" algorithm for evaluating AND/OR trees and the Alpha-Beta pruning algorithm for evaluating MIN/MAX trees. We prove that the algorithm achieves a linear speed-up over the left-to-right algorithm on uniform AND/OR trees when the number of processors used is close to the height of the input tree. We conjecture that the same conclusion holds for the speed-up of the algorithm over the Alpha-Beta pruning algorithm.