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Primal Separation for 0/1 Polytopes

Eisenbrand, F., Rinaldi, G., & Ventura, P. (2003). Primal Separation for 0/1 Polytopes. Mathematical Programming / A, 95, 475-491.

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Genre: Journal Article

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Creators:
Eisenbrand, Friedrich1, Author
Rinaldi, Giovanni2, Author
Ventura, Paolo3, Author
Affiliations:
1Discrete Optimization, MPI for Informatics, Max Planck Society, ou_1116548
2External Organizations, ou_persistent22
3Machine Learning, MPI for Informatics, Max Planck Society, ou_1116552

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Abstract: \noindent The 0/1~primal separation problem is: Given an extreme point $\bar{x}$ of a 0/1~polytope $P$ and some point $x^*$, find an inequality which is tight at $\bar{x}$, 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 $P$. \noindent 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. \noindent 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.

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Language(s): eng - English
Dates: 2004-07-062003
Publication Status: Published in print
Pages: -
Publishing info: -
Rev. Type: Peer
Identifiers: eDoc: 201831
Degree: -

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### Source 1

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Title: Mathematical Programming / A
Source Genre: Journal
Creator(s):
Affiliations:
Publ. Info: Heidelberg : North-Holland
Pages: - Volume / Issue: 95 Sequence Number: - Start / End Page: 475 - 491 Identifier: ISSN: 0025-5610
CoNE: https://pure.mpg.de/cone/journals/resource/954928560452