Polynomial time solvable algorithms to a class of unconstrained and linearly constrained binary quadratic programming problems

Binary quadratic programming (BQP) is a typical integer programming problem widely applied in the field of signal processing, economy, management and engineering. However, it is NP-hard and lacks efficient algorithms. Due to this reason, in this paper, some novel polynomial algorithms are proposed t...

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Bibliographic Details
Published in:Neurocomputing (Amsterdam) Vol. 198; pp. 171 - 179
Main Authors: Gu, Shenshen, Cui, Rui, Peng, Jiao
Format: Journal Article
Language:English
Published: Elsevier B.V 19.07.2016
Subjects:
Algorithms
Binary quadratic programming
Constraints
Dynamic programming
Economics
Integer programming
Management
Polynomial time solvable algorithm
Polynomials
Quadratic programming
Signal processing
Polynomial time solvable algorithm
Binary quadratic programming
Dynamic programming
ISSN:0925-2312, 1872-8286
Online Access:Get full text
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Summary:Binary quadratic programming (BQP) is a typical integer programming problem widely applied in the field of signal processing, economy, management and engineering. However, it is NP-hard and lacks efficient algorithms. Due to this reason, in this paper, some novel polynomial algorithms are proposed to solve a class of unconstrained and linearly constrained binary quadratic programming problems. We first deduce the polynomial time solvable algorithms to the unconstrained binary quadratic programming problems with Q being a seven-diagonal matrix (UBQP7) and a five-diagonal matrix (UBQP5) respectively with two different approaches. Then, the algorithm to unconstrained problem is combined with the dynamic programming method to solve the linearly constrained binary quadratic programming problem with Q being a five-diagonal matrix (LCBQP5). In addition, the polynomial solvable feature of these algorithms is analyzed and some specific examples are presented to illustrate these new algorithms. Lastly, we demonstrate their polynomial feature as well as their high efficiency.
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ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2015.09.130