Two-variable linear programming in parallel
Danny Z. Chen,Jinhui Xu +1 more
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TLDR
This paper presents 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.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.read more
Citations
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Proceedings ArticleDOI
Parallelism in Randomized Incremental Algorithms
TL;DR: In this article, it was shown that most sequential randomized incremental algorithms are in fact parallel, and the dependence structure is shallow for all of the algorithms, implying high parallelism, and three types of dependences found in the algorithms studied and presented a framework for analyzing each type of algorithm.
Posted Content
Parallelism in Randomized Incremental Algorithms
TL;DR: It is shown that most sequential randomized incremental algorithms are in fact parallel, and three types of dependences found in the algorithms studied are identified and a framework for analyzing each type of algorithm is presented.
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On simplex method with most-obtuse-angle rule and cosine rule
TL;DR: This paper shows that the cosine rule used in this class of simplex methods is equivalent to the most-obtuse-angle pivot rule, proposed by Pan (1990) [6].
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Parallelism in Randomized Incremental Algorithms
TL;DR: This article shows the first incremental Delaunay triangulation algorithm with optimal work and polylogarithmic depth, and identifies three types of algorithms based on their dependencies and presents a framework for analyzing each type.
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Parallel Algorithms for Partitioning Sorted Sets and Related Problems
TL;DR: The complexity bounds of the parallel partition algorithm on the respective special cases match those of the optimal EREW PRAM algorithms for merging, sorting, and finding an approximate median.
References
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TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
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TL;DR: This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more.
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TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
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Introduction to algorithms: 4. Turtle graphics
TL;DR: In this article, a language similar to logo is used to draw geometric pictures using this language and programs are developed to draw geometrical pictures using it, which is similar to the one we use in this paper.
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Algorithms in Combinatorial Geometry
TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.