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International Symposium on Fundamentals of Computation Theory

FCT 2013: Fundamentals of Computation Theory pp 271–282Cite as

Domination Analysis of Algorithms for Bipartite Boolean Quadratic Programs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8070))

Abstract

For the bipartite boolean quadratic programming problem (BBQP) with m + n variables, an O(mn) algorithm is given to compute the average objective function value \(\mathcal{A}\) of all solutions where as computing the median objective function value is shown to be NP-hard. Also, we show that any solution with objective function value no worse than \(\mathcal{A}\) dominates at least 2m + n − 2 solutions and this bound is the best possible. An O(mn) algorithm is given to identify such a solution. We then show that for any fixed rational number \(\alpha=\frac{a}{b} > 1\) and gcd(a,b) = 1, no polynomial time approximation algorithm exists for BBQP with dominance ratio larger than \(1-2^{\frac{(1-\alpha)}{\alpha}(m+n)}\), unless P=NP. Finally, it is shown that some powerful local search algorithms can get trapped at a local maximum with objective function value less than \(\mathcal{A}\).

This work was supported by an NSERC discovery grant awarded to Abraham P. Punnen.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University Surrey, 250-13450 102nd AV, Surrey, British Columbia, V3T 0A3, Canada

    Abraham P. Punnen, Piyashat Sripratak & Daniel Karapetyan

Authors
  1. Abraham P. Punnen
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  2. Piyashat Sripratak
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  3. Daniel Karapetyan
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Editors and Affiliations

  1. Computer Science, University of Liverpool, Ashton Street, L69 3BX, Liverpool, UK

    Leszek Gąsieniec

  2. Department of Computer Science, University of Liverpool, United Kingdom

    Frank Wolter

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Punnen, A.P., Sripratak, P., Karapetyan, D. (2013). Domination Analysis of Algorithms for Bipartite Boolean Quadratic Programs. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-40164-0_26

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