*Vipin Kumar, K. Ramesh, V. Nageshwara Rao*

This paper presents many different parallel formulations of the A*/Branch-and-Bound search algorithm. The parallel formulations primarily differ in the data structures used. Some formulations are suited only for shared-memory architectures, whereas others are suited for distributed-memory architectures as well. These parallel formulations have been implemented to solve the vertex cover problem and the TSP problem on the BBN Butterfly parallel processor. Using appropriate data structures, we are able to obtain fairly linear speedups for as many as 100 processors. We also discovered problem characteristics that make certain formulations more (or less) suitable for some search problems. Since the best-first search paradigm of A*/Branch-and-Bound is very commonly used, we expect these parallel formulations to be effective for a variety of problems. Concurrent and distributed priority queues used in these parallel formulations can be used in many parallel algorithms other than parallel A*/branch-and-bound.

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