Faster exact solution of sparse MaxCut and QUBO problems

The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years. This article aims to advance the...

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Veröffentlicht in:Mathematical programming computation Jg. 15; H. 3; S. 445 - 470
Hauptverfasser: Rehfeldt, Daniel, Koch, Thorsten, Shinano, Yuji
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Springer Nature B.V
Schlagworte:
Algorithms
Combinatorial analysis
Exact solutions
Full Length Paper
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Quantum computers
Solvers
Theory of Computation
90C10
90C27
Maximum-cut
Branch-and-cut
Quadratic unconstrained binary optimization
ISSN:1867-2949, 1867-2957
Online-Zugang:Volltext
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Zusammenfassung:The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years. This article aims to advance the state of the art in the exact solution of both problems—by using mathematical programming techniques. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse maximum-cut and quadratic unconstrained binary optimization instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.
Bibliographie:ObjectType-Article-1
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ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-023-00236-6