From SAT to Maximum Independent Set: A New Approach to Characterize Tractable Classes

14 pages•Published: May 4, 2017

Yazid Boumarafi, Lakhdar Sais and Yakoub Salhi

Abstract

In this paper, we propose a new approach for defining tractable classes in propositional satisfiability problem (in short SAT). The basic idea consists in transforming SAT instances into instances of the problem of finding a maximum independent set. In this context, we only consider propositional formulæ in conjunctive normal form where each clause is either positive or binary negative. Tractable classes are obtained from existing polynomial time algorithms of the problem of finding a maximum independent set in the case of different graph classes, such as claw-free graphs and perfect graphs. We show, in particular, that the pigeonhole principle belongs to one of the defined tractable classes. Furthermore, we propose a characterization of the minimal models in the largest considered fragment based on the maximum independent set problem.

Keyphrases: maximum independent set, propositional satisfiability, tractable classes

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 286-299.

Links:	https://easychair.org/publications/paper/65
	https://doi.org/10.29007/c9f6

BibTeX entry

@inproceedings{LPAR-21:From_SAT_Maximum_Independent,
  author    = {Yazid Boumarafi and Lakhdar Sais and Yakoub Salhi},
  title     = {From SAT to Maximum Independent Set: A New Approach to Characterize Tractable Classes},
  booktitle = {LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Thomas Eiter and David Sands},
  series    = {EPiC Series in Computing},
  volume    = {46},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/65},
  doi       = {10.29007/c9f6},
  pages     = {286-299},
  year      = {2017}}

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