On the relative strength of split, triangle and quadrilateral cuts

• 成果类型: Article
• 署名作者: Basu, Amitabh; Bonami, Pierre; Cornuejols, Gerard; Margot, Francois
• 署名单位: Carnegie Mellon University; Aix-Marseille Universite
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0281-x
• 发表日期: 2011
• 页码: 281-314
• 关键词: programming-problems; inequalities; closure

摘要

Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in a well defined sense, triangle inequalities provide a good approximation of the integer hull. The same statement holds for quadrilateral inequalities. On the other hand, the approximation produced by split inequalities may be arbitrarily bad.