# Item

ITEM ACTIONSEXPORT

**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.

### Basic

show hide**Item Permalink:**http://hdl.handle.net/11858/00-001M-0000-000F-2DCB-F

**Version Permalink:**http://hdl.handle.net/11858/00-001M-0000-0024-C113-A

**Genre:**Journal Article

### Files

show Files### Locators

show### Content

show
hide

**Free keywords:**-

**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.

### Details

show
hide
Modified: 2004-07-06Published in Print: 2003

Other: Local-ID: C1256BDD00205AD6-873105CA3E3DF24BC1256CAA003307EF-ERV2003

**Language(s):**eng - English

**Dates:**

**Publication Status:**Published in print

**Pages:**-

**Publishing info:**-

**Table of Contents:**-

**Rev. Type:**Peer

**Identifiers:**eDoc: 201831

Other: Local-ID: C1256BDD00205AD6-873105CA3E3DF24BC1256CAA003307EF-ERV2003

**Degree:**-

### Event

show### Legal Case

show### Project information

show### Source 1

show
hide

CoNE: https://pure.mpg.de/cone/journals/resource/954928560452

**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: 0025-5610CoNE: https://pure.mpg.de/cone/journals/resource/954928560452