Affiliation:
1. University of Cambridge
2. University of Cambridge, Cambridge, UK
Abstract
We show that the ellipsoid method for solving linear programs can be implemented in a way that respects the symmetry of the program being solved. That is to say, there is an algorithmic implementation of the method that does not distinguish, or make choices, between variables or constraints in the program unless they are distinguished by properties definable from the program. In particular, we demonstrate that the solvability of linear programs can be expressed in fixed-point logic with counting (FPC) as long as the program is given by a separation oracle that is itself definable in FPC. We use this to show that the size of a maximum matching in a graph is definable in FPC. This settles an open problem first posed by Blass, Gurevich and Shelah [Blass et al. 1999]. On the way to defining a suitable separation oracle for the maximum matching program, we provide FPC formulas defining canonical maximum flows and minimum cuts in undirected capacitated graphs.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference44 articles.
1. Maximum Matching and Linear Programming in Fixed-Point Logic with Counting
2. Affine systems of equations and counting infinitary logic
3. Sherali-Adams relaxations and indistinguishability in counting logics
4. A. Blass and Y. Gurevich. 2005. A quick update on open problems in Blass-Gurevich-Shelah's article ‘On polynomial time computations over unordered structures’. Online at http://research.microsoft.com/_gurevich/annotated.html. A. Blass and Y. Gurevich. 2005. A quick update on open problems in Blass-Gurevich-Shelah's article ‘On polynomial time computations over unordered structures’. Online at http://research.microsoft.com/_gurevich/annotated.html.
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献