Abstract.
Given m ordered segments that form a partition of some universe (e.g., a two-dimensional strip), the multisearch problem consists of determining, for a set of n query points in the universe, the segments they belong to. We present the first nontrivial parallel deterministic scheme for performing multisearch on a distributed-memory machine when m=ω(n) . The scheme is designed on the BSP* model of parallel computation, a variant of Valiant's BSP which rewards blockwise communication, and relies on a suitable redundant representation of the segments. The time needed to answer the queries is analyzed as a function of the redundancy and of the BSP* parameters. We show that optimal performance can be obtained using logarithmic redundancy. We also prove a lower bound on the communication requirements of any deterministic multisearch scheme realized on a distributed-memory machine. The lower bound exhibits a tradeoff between the redundancy used to represent the segments and the performance of the scheme.
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Received June 1, 1997; revised March 10, 1998.
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Bäumker, A., Dittrich, W. & Pietracaprina, A. The Complexity of Parallel Multisearch on Coarse-Grained Machines . Algorithmica 24, 209–242 (1999). https://doi.org/10.1007/PL00008261
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DOI: https://doi.org/10.1007/PL00008261