NDLI: Primal separation for 0/1 polytopes

Content Provider	Springer Nature Link
Author	Eisenbrand, Friedrich Rinaldi, Giovanni Ventura, Paolo
Copyright Year	2003
Abstract	The 0/1 primal separation problem is: Given an extreme point x¯ of a 0/1 polytope P and some point x , find an inequality which is tight at x¯, violated by x and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time.
Starting Page	475
Ending Page	491
Page Count	17
File Format	PDF
ISSN	00255610
Journal	Mathematical Programming
Volume Number	95
Issue Number	3
e-ISSN	14364646
Language	English
Publisher	Springer-Verlag
Publisher Date	2003-03-01
Publisher Place	Berlin Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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