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Hybrid Parallelization of Standard Full Tableau Simplex Method with MPI and OpenMP

Published: 02 October 2014 Publication History

Abstract

The simplex method has been successfully used in solving linear programming problems for many years. Parallel approaches have also extensively been studied due to the intensive computations required, especially for the solution of large linear problems (LPs). In this paper we present a highly scalable implementation framework of the standard full tableau simplex method on a hybrid parallel environment, which consists of multiple multicore processing nodes interconnected via a high-speed communication network. Specifically, we have designed and implemented a suitable column-based distribution scheme, following three different parallelization models: (a) pure MPI (one MPI process on each core), (b) hybrid OpenMP-based (OpenMP constructs used for parallelization over the cores of each node), and (c) hybrid MPI-based (MPI 3.0 shared memory functions used for parallelization over the cores of each node). We then compare our approaches (i) among each other for variable number of nodes/cores and problem size, and (ii) to other recent and valuable corresponding efforts in the literature. In all cases the hybrid OpenMP-based parallelization scheme performs quite/much better than the other two schemes. Moreover, all the three parallelization schemes lead to particularly high speed-up and efficiency values, whereas the corresponding values for the OpenMP-based scheme are considerably better than the ones achieved in other similar research efforts and implementations.

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Cited By

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  • (2015)Advances in the Parallelization of the Simplex MethodAlgorithms, Probability, Networks, and Games10.1007/978-3-319-24024-4_17(281-307)Online publication date: 22-Nov-2015

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Published In

cover image ACM Other conferences
PCI '14: Proceedings of the 18th Panhellenic Conference on Informatics
October 2014
355 pages
ISBN:9781450328975
DOI:10.1145/2645791
  • General Chairs:
  • Katsikas Sokratis,
  • Hatzopoulos Michael,
  • Apostolopoulos Theodoros,
  • Anagnostopoulos Dimosthenis,
  • Program Chairs:
  • Carayiannis Elias,
  • Varvarigou Theodora,
  • Nikolaidou Mara
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

In-Cooperation

  • Greek Com Soc: Greek Computer Society
  • Univ. of Piraeus: University of Piraeus
  • National and Kapodistrian University of Athens: National and Kapodistrian University of Athens
  • Athens U of Econ & Business: Athens University of Economics and Business

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 02 October 2014

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Author Tags

  1. Linear Programming
  2. MPI
  3. OpenMP
  4. Parallel Processing
  5. Simplex Algorithm

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PCI '14

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PCI '14 Paper Acceptance Rate 51 of 102 submissions, 50%;
Overall Acceptance Rate 190 of 390 submissions, 49%

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Cited By

View all
  • (2015)Advances in the Parallelization of the Simplex MethodAlgorithms, Probability, Networks, and Games10.1007/978-3-319-24024-4_17(281-307)Online publication date: 22-Nov-2015

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