Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model

Reviewer: Michael G. Murphy

The authors address the design and analysis of specific parallel algorithms with the goal of obtaining tight bounds on their speed-ups on actual machines. Part of the approach is an extension of Valiant's bulk synchronous parallel (BSP) model, BSP*, which rewards blockwise communication. They also use Valiant's notion of 1-optimality, which intuitively means that a 1-optimal parallel algorithm for p processors achieves a speed-up of approximately p . The problem considered is the multisearch problem, in which a 2D strip is partitioned into m segments and, given n query points, the task is to locate the segment for each query. The authors present a deterministic BSP* algorithm (many search queries and other constraints) that is 1-optimal and a randomized BSP* algorithm (few search queries and other constraints) that is 1-optimal with high probability. Implementation results are also presented. Previous parallel algorithms for the multisearch problem were not 1-optimal and did not use blockwise communication. Because of the authors' concern regarding real machines, and to reflect the reality of a truly finite number of processors (for example, a 1000-processor MIMD machine is large), BSP* and 1-optimality were chosen to overcome the PRAM cost model, since communication is more expensive than internal computation on real parallel machines. The multisearch problem was chosen as a representative computational geometry problem with numerous applications. The paper is organized into six sections: an introduction; an outline of the algorithm and notation; communication routines; multisearch with many queries; multisearch with few queries; and experiments. The bibliography lists 17 references. The paper is well organized, well written, and appropriately rigorous. Researchers with an interest in efficient parallel algorithms on real parallel machines are the intended audience.