A Branch and Cut solver for the maximum stable set problem
A Branch and Cut solver for the maximum stable set problem
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DOI：
10.1007/s10878-009-9264-3
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发表时间：
2011-05
影响因子：
1
通讯作者：
Steffen Rebennack;M. Oswald;D. Theis;Hanna Seitz;G. Reinelt;P. Pardalos
中科院分区：
文献类型：
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作者：
Steffen Rebennack;M. Oswald;D. Theis;Hanna Seitz;G. Reinelt;P. Pardalos
本文讨论了最大稳定集问题的割平面法。我们提供的理论结果方面的定义属性的不等式得到一个已知的项目和升降式分离方法称为边缘投影，及其变种。一个分支和切割算法的实现，它使用边缘投影和其他两个分离工具，已讨论了其他问题：本地切割（由Applegate，Bixby，Chvátal和库克开创）和mod-kcuts。我们比较这种方法的性能，另一个由罗西和Smiriglio（歌剧。保留信函28：63-74，2001）并讨论我们测试过的工具的价值。
This paper deals with the cutting-plane approach to the maximum stable set problem. We provide theoretical results regarding the facet-defining property of inequalities obtained by a known project-and-lift-style separation method called edge-projection, and its variants. An implementation of a Branch and Cut algorithm is described, which uses edge-projection and two other separation tools which have been discussed for other problems: local cuts (pioneered by Applegate, Bixby, Chvátal and Cook) and mod-kcuts. We compare the performance of this approach to another one by Rossi and Smiriglio (Oper. Res. Lett. 28:63–74, 2001) and discuss the value of the tools we have tested.