Solving Totally Unimodular LPs with the Shadow Vertex Algorithm.
Leibniz International Proceedings in Informatics(2015)
摘要
We show that the shadow vertex simplex algorithm can be used to solve linear programs in strongly polynomial time with respect to the number n of variables, the number m of constraints, and 1/delta, where delta is a parameter that measures the flatness of the vertices of the polyhedron. This extends our recent result that the shadow vertex algorithm finds paths of polynomial length (w.r.t. n, m, and 1/delta) between two given vertices of a polyhedron [4]. Our result also complements a recent result due to Eisenbrand and Vempala [6] who have shown that a certain version of the random edge pivot rule solves linear programs with a running time that is strongly polynomial in the number of variables n and 1/delta, but independent of the number m of constraints. Even though the running time of our algorithm depends on m, it is significantly faster for the important special case of totally unimodular linear programs, for which 1/delta <= n and which have only O(n(2)) constraints.
更多查看译文
关键词
linear optimization,simplex algorithm,shadow vertex method
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要