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Two-variable linear programming in parallel

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Algorithm Theory — SWAT'98 (SWAT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1432))

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Abstract

Two-variable linear programming is a fundamental problem in computational geometry. Sequentially, this problem was solved optimally in linear time by Megiddo and Dyer using the elegant prune-and-search technique. In parallel, the previously best known deterministic algorithm on the EREW PRAM for this problem takes O(log n log log n) time and O(n) work. In this paper, we present a faster parallel deterministic two-variable linear programming algorithm, which takes O(log n log* n) time and O(n) work on the EREW PRAM. Our algorithm is based on an interesting parallel prune-and-search technique, and makes use of new geometric observations which can be viewed as generalizations of those used by Megiddo and Dyer's sequential algorithms. Our parallel prune-and-search technique also leads to efficient EREW PRAM algorithms for other problems, and is likely to be useful in solving more problems.

This research was supported in part by the National Science Foundation under Grant CCR-9623585.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, 46556, Notre Dame, IN, USA

    Danny Z. Chen & Jinhui Xu

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  1. Danny Z. Chen
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  2. Jinhui Xu
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Stefan Arnborg Lars Ivansson

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© 1998 Springer-Verlag Berlin Heidelberg

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Chen, D.Z., Xu, J. (1998). Two-variable linear programming in parallel. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054365

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  • DOI: https://doi.org/10.1007/BFb0054365

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  • Print ISBN: 978-3-540-64682-2

  • Online ISBN: 978-3-540-69106-8

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