Domination Analysis of Algorithms for Bipartite Boolean Quadratic Programs

Punnen, Abraham P.; Sripratak, Piyashat; Karapetyan, Daniel

doi:10.1007/978-3-642-40164-0_26

Cited by 3 publications

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“…To the best of our knowledge, BQP01 has not been thoroughly investigated in literature, especially from the point of view of polynomially solvable special cases. Some recent references on the problem considers theoretical analysis of approximation algorithms [30] and experimental analysis of heuristics [14,18]. The primary focus of this work is to identify polynomially solvable special cases of BQP01.…”

Section: Introductionmentioning

confidence: 99%

The bipartite unconstrained 0–1 quadratic programming problem: Polynomially solvable cases

Punnen

Sripratak

Karapetyan

2015

Discrete Applied Mathematics

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a b s t r a c tWe consider the bipartite unconstrained 0-1 quadratic programming problem (BQP01) which is a generalization of the well studied unconstrained 0-1 quadratic programming problem (QP01). BQP01 has numerous applications and the problem is known to be MAX SNP hard. We show that if the rank of an associated m×n cost matrix Q = (q ij ) is fixed, then BQP01 can be solved in polynomial time. When Q is of rank one, we provide an O(n log n) algorithm and this complexity reduces to O(n) with additional assumptions. Further, if q ij = a i + b j for some a i and b j , then BQP01 is shown to be solvable in O(mn log n) time. By restricting m = O(log n), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m = O( k √ n) for a fixed k. Finally, if the minimum number of rows and columns to be deleted from Q to make the remaining matrix nonnegative is O(log n), then we show that BQP01 is polynomially solvable but it is NP-hard if this number is O( k √ n) for any fixed k.

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Section: Introductionmentioning

confidence: 99%