Domination analysis of algorithms for bipartite boolean quadratic programs

  • Authors:

  • Abraham P. Punnen;Piyashat Sripratak;Daniel Karapetyan

  • Affiliations:

  • Department of Mathematics, Simon Fraser University Surrey, Surrey, British Columbia, Canada;Department of Mathematics, Simon Fraser University Surrey, Surrey, British Columbia, Canada;Department of Mathematics, Simon Fraser University Surrey, Surrey, British Columbia, Canada

  • Venue:
  • FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
  • Year:
  • 2013

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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 $\mathcal{A}$.