Parallel Heuristic Search: Two Approaches

Abstract

We explore two approaches to parallel heuristic search: one based on tree decomposition, in which different processors search different parts of the tree, and the other based on parallel window search, in which each processor searches the whole tree but with different cost bounds. In the first, we present a generic distributed tree search algorithm that effectively searches irregular trees using an arbitrary number of processors without shared memory or centralized control. For brute-force search the algorithm achieves almost linear speedup. For alpha-beta search, the straightforward approach of allocating P processors in a breadth-first manner achieves an overall speedup with random node ordering of P ^.75 . Furthermore we present a novel processor allocation strategy, called Bound-and-Branch, for parallel alpha-beta search that achieves linear speedup in the case of perfect node ordering. In practice, we achieve a speedup of 12 with 32 processors on a 32-node Hypercube multiprocessor for the game of Othello.

In the second approach, we show how node ordering can be combined with parallel window search to quickly find a near-optimal solution to single-agent problems. First, we show how node ordering by maximum g among nodes with equal f = g + h values can improve the performance of iterative-deepening-A* (IDA*). We then consider a window search where different processes perform IDA* simultaneously on the same problem but with different cost thresholds. Next, we combine the two ideas to produce a parallel window search algorithm in which node ordering information is shared among the different processes. Finally, we show how to combine distributed tree search with parallel window search in single-agent or two-player game searches.

This chapter is based upon two articles [FERG88] and [POWL89] that appeared originally in AAAI 88 and IJCAI 89 proceedings. This research was supported by an NSF Presidential Young Investigator Award to the third author, NSF grant IRI- 8801939; by an Intel Hypercube, JPL contract number 957523; by DARPA contract MDA 903-87-C0663; and by a Hewlett-Packard equipment grant.