On the Structure of Industrial SAT Instances
- Carlos AnsóteguiAffiliated withUniversitat de Lleida (DIEI, UdL)
- , María Luisa BonetAffiliated withUniversitat Politècnica de Catalunya (LSI, UPC)
- , Jordi LevyAffiliated withArtificial Intelligence Research Institute (IIIA, CSIC)
During this decade, it has been observed that many real-world graphs, like the web and some social and metabolic networks, have a scale-free structure. These graphs are characterized by a big variability in the arity of nodes, that seems to follow a power-law distribution. This came as a big surprise to researchers steeped in the tradition of classical random networks.
SAT instances can also be seen as (bi-partite) graphs. In this paper we study many families of industrial SAT instances used in SAT competitions, and show that most of them also present this scale-free structure. On the contrary, random SAT instances, viewed as graphs, are closer to the classical random graph model, where arity of nodes follows a Poisson distribution with small variability. This would explain their distinct nature.
We also analyze what happens when we instantiate a fraction of the variables, at random or using some heuristics, and how the scale-free structure is modified by these instantiations. Finally, we study how the structure is modified during the execution of a SAT solver, concluding that the scale-free structure is preserved.
- On the Structure of Industrial SAT Instances
- Book Title
- Principles and Practice of Constraint Programming - CP 2009
- Book Subtitle
- 15th International Conference, CP 2009 Lisbon, Portugal, September 20-24, 2009 Proceedings
- pp 127-141
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Ian P. Gent (16)
- Editor Affiliations
- 16. School of Computer Science, University of St. Andrews
- Author Affiliations
- 17. Universitat de Lleida (DIEI, UdL),
- 18. Universitat Politècnica de Catalunya (LSI, UPC),
- 19. Artificial Intelligence Research Institute (IIIA, CSIC),
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