稀疏MaxCut和QUBO问题的快速精确解
Faster exact solution of sparse MaxCut and QUBO problems
摘要：
最大割问题是组合优化的基本问题之一。随着量子计算机的出现，最大割和等价的二次无约束二元最优化问题近年来引起了人们的极大兴趣。本文旨在通过在数字计算机上使用数学规划技术来推进这两个问题的精确解的最新技术水平。主要的重点在于稀疏的问题实例，虽然也可以解决密集的问题。我们增强了几个算法组件，如减少技术和切割平面分离算法，并将它们结合在一个精确的分支和切割求解器。此外，我们提供了一个并行的实现。新的求解器显着优于现有的最先进的软件稀疏MaxCut和QUBO实例。此外，我们还改进了第七届DIMACS挑战赛和QPLIB中几个实例的最佳边界，并首次将其中一些解决为最优。
英文摘要：
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 on digital computers. 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 MaxCut and QUBO 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.
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