- Author:
- Yanjun Zhang,
- Chairman:
- Richard M. Karp
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.
Cited By
- Colombo G and Allen S (2018). A comparison of problem decomposition techniques for the FAP, Journal of Heuristics, 16:3, (259-288), Online publication date: 1-Jun-2010.
Blumofe R and Leiserson C Space-efficient scheduling of multithreaded computations Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing, (362-371)- Ranade A Optimal speedup for backtrack search on a butterfly network Proceedings of the third annual ACM symposium on Parallel algorithms and architectures, (40-48)
- Broder A, Karlin A, Raghavan P and Upfal E On the parallel complexity of evaluating game trees Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms, (404-413)
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