Linear-programming design and analysis of fast algorithms for Max 2-CSP
| Autor: | Gregory B. Sorkin, Alex Scott |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Polynomial
Linear programming Maximum cut 0211 other engineering and technologies Binary number 0102 computer and information sciences 02 engineering and technology 01 natural sciences Theoretical Computer Science Combinatorics Linear-programming duality Overhead (computing) Constraint satisfaction problem Max 2-Sat Mathematics Max Cut Discrete mathematics 021103 operations research Degree (graph theory) Applied Mathematics Measure and conquer Treewidth Computational Theory and Mathematics 010201 computation theory & mathematics Max 2-CSP Algorithm Exact algorithms |
| Popis: | The class Max (r, 2)-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two r-valued variables per clause. For instances with n variables and m binary clauses, we present an O (n r 5 + 19 m / 100)-time algorithm which is the fastest polynomial-space algorithm for many problems in the class, including Max Cut. The method also proves a treewidth bound tw (G) ≤ (13 / 75 + o (1)) m, which gives a faster Max 2-CSP algorithm that uses exponential space: running in time O {star operator} (2 (13 / 75 + o (1)) m), this is fastest for most problems in Max 2-CSP. Parametrizing in terms of n rather than m, for graphs of average degree d we show a simple algorithm running time O {star operator} (2 (1 - frac(2, d + 1)) n), the fastest polynomial-space algorithm known. In combination with "Polynomial CSPs" introduced in a companion paper, these algorithms also allow (with an additional polynomial factor overhead in space and time) counting and sampling, and the solution of problems like Max Bisection that escape the usual CSP framework. Linear programming is key to the design as well as the analysis of the algorithms. © 2007 Elsevier Ltd. All rights reserved. |
| Databáze: | OpenAIRE |
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