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Combinatorial Optimization Using Electro-Optical Vector by Matrix Multiplication Architecture

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Optical SuperComputing (OSC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5882))

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Abstract

A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Texas State University, San Marcos, Texas, 78666, USA

    Dan E. Tamir

  2. Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva, 84105, Israel

    Natan T. Shaked

  3. Department of Physics, Texas State University, San Marcos, Texas, 78666, USA

    Wilhelmus J. Geerts

  4. Department of Computer Science, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva, 84105, Israel

    Shlomi Dolev

Authors
  1. Dan E. Tamir
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  2. Natan T. Shaked
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  3. Wilhelmus J. Geerts
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  4. Shlomi Dolev
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ben Gurion University of the Negev, Beer-Sheva, Israel

    Shlomi Dolev

  2. Department of Computer Science, Faculty of Mathematics and Computer Science, BabeÅŸ-Bolyai University, Cluj-Napoca, Romania

    Mihai Oltean

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© 2009 Springer-Verlag Berlin Heidelberg

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Tamir, D.E., Shaked, N.T., Geerts, W.J., Dolev, S. (2009). Combinatorial Optimization Using Electro-Optical Vector by Matrix Multiplication Architecture. In: Dolev, S., Oltean, M. (eds) Optical SuperComputing. OSC 2009. Lecture Notes in Computer Science, vol 5882. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10442-8_17

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  • DOI: https://doi.org/10.1007/978-3-642-10442-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10441-1

  • Online ISBN: 978-3-642-10442-8

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