The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases
© 2015 Elsevier B.V. All rights reserved. We 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 har...
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th-cmuir.6653943832-441642018-04-25T07:46:22Z The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases Abraham P. Punnen Piyashat Sripratak Daniel Karapetyan Agricultural and Biological Sciences © 2015 Elsevier B.V. All rights reserved. We 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=( qij ) is fixed, then BQP01 can be solved in polynomial time. When Q is of rank one, we provide an O(nlogn) algorithm and this complexity reduces to O(n) with additional assumptions. Further, if qij = ai + bj for some ai and bj , then BQP01 is shown to be solvable in O(mnlogn) time. By restricting m=O(logn), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m=O(nk) for a fixed k. Finally, if the minimum number of rows and columns to be deleted from Q to make the remaining matrix non-negative is O(logn), then we show that BQP01 is polynomially solvable but it is NP-hard if this number is O(nk) for any fixed k. 2018-01-24T04:38:50Z 2018-01-24T04:38:50Z 2015-10-01 Journal 0166218X 2-s2.0-84938291413 10.1016/j.dam.2015.04.004 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84938291413&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44164 |
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Agricultural and Biological Sciences Abraham P. Punnen Piyashat Sripratak Daniel Karapetyan The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases |
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© 2015 Elsevier B.V. All rights reserved. We 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=( qij ) is fixed, then BQP01 can be solved in polynomial time. When Q is of rank one, we provide an O(nlogn) algorithm and this complexity reduces to O(n) with additional assumptions. Further, if qij = ai + bj for some ai and bj , then BQP01 is shown to be solvable in O(mnlogn) time. By restricting m=O(logn), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m=O(nk) for a fixed k. Finally, if the minimum number of rows and columns to be deleted from Q to make the remaining matrix non-negative is O(logn), then we show that BQP01 is polynomially solvable but it is NP-hard if this number is O(nk) for any fixed k. |
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Abraham P. Punnen Piyashat Sripratak Daniel Karapetyan |
author_facet |
Abraham P. Punnen Piyashat Sripratak Daniel Karapetyan |
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Abraham P. Punnen |
title |
The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases |
title_short |
The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases |
title_full |
The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases |
title_fullStr |
The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases |
title_full_unstemmed |
The bipartite unconstrained 0-1 quadratic programming problem: Polynomially solvable cases |
title_sort |
bipartite unconstrained 0-1 quadratic programming problem: polynomially solvable cases |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84938291413&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44164 |
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