### Abstract

Prior algorithms known for exactly solving MAX 2-SAT improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted MAX 2-SAT instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-SAT instance F with n variables, the worst case running time is Õ(2^{1-1/(d̃(F)_1))n}), where d̃(F) is the average degree in the constraint graph defined by F. We use strict α-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like MAX 3-SAT and MAX CUT. We also introduce a notion of strict (α, β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for MAX k-SAT and MAX k-LIN-2.

Original language | English (US) |
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Title of host publication | SOFSEM 2007 |

Subtitle of host publication | Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings |

Pages | 272-283 |

Number of pages | 12 |

State | Published - Dec 1 2007 |

Event | 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007 - Harrachov, Czech Republic Duration: Jan 20 2007 → Jan 26 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4362 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007 |
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Country | Czech Republic |

City | Harrachov |

Period | 1/20/07 → 1/26/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*SOFSEM 2007: Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings*(pp. 272-283). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4362 LNCS).

}

*SOFSEM 2007: Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4362 LNCS, pp. 272-283, 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007, Harrachov, Czech Republic, 1/20/07.

**Exact MAX 2-SAT : Easier and faster.** / Fürer, Martin; Kasiviswanathan, Shiva Prasad.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Exact MAX 2-SAT

T2 - Easier and faster

AU - Fürer, Martin

AU - Kasiviswanathan, Shiva Prasad

PY - 2007/12/1

Y1 - 2007/12/1

N2 - Prior algorithms known for exactly solving MAX 2-SAT improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted MAX 2-SAT instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-SAT instance F with n variables, the worst case running time is Õ(21-1/(d̃(F)_1))n), where d̃(F) is the average degree in the constraint graph defined by F. We use strict α-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like MAX 3-SAT and MAX CUT. We also introduce a notion of strict (α, β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for MAX k-SAT and MAX k-LIN-2.

AB - Prior algorithms known for exactly solving MAX 2-SAT improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted MAX 2-SAT instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-SAT instance F with n variables, the worst case running time is Õ(21-1/(d̃(F)_1))n), where d̃(F) is the average degree in the constraint graph defined by F. We use strict α-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like MAX 3-SAT and MAX CUT. We also introduce a notion of strict (α, β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for MAX k-SAT and MAX k-LIN-2.

UR - http://www.scopus.com/inward/record.url?scp=36448936802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36448936802&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:36448936802

SN - 9783540695066

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 272

EP - 283

BT - SOFSEM 2007

ER -