A special role of Boolean quadratic polytopes among other combinatorial polytopes
We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we us...
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| Vydáno v: | arXiv.org |
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| Hlavní autor: | |
| Médium: | Paper |
| Jazyk: | angličtina |
| Vydáno: |
Ithaca
Cornell University Library, arXiv.org
05.03.2015
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| Témata: | |
| ISSN: | 2331-8422 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family \(P\) is affinely reduced to a family \(Q\) if for every polytope \(p\in P\) there exists \(q\in Q\) such that \(p\) is affinely equivalent to \(q\) or to a face of \(q\), where \(\dim q = O((\dim p)^k)\) for some constant \(k\). Under this comparison the above-mentioned families are splitted into two equivalence classes. We show also that these two classes are simpler (in the above sence) than the families of poytopes of the following problems: set covering, traveling salesman, 0-1 knapsack problem, 3-satisfiability, cubic subgraph, partial ordering. In particular, Boolean quadratic polytopes appear as faces of polytopes in every of the mentioned families. |
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| Bibliografie: | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.1408.0948 |