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Spines of random constraint satisfaction problems: definition and connection with computational complexity

Spines of random constraint satisfaction problems: definition and connection with computational... We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited connection between the two phenomena indeed exists. Specifically, we extend the definition of the spine order parameter of Bollobás et al. [10] to random constraint satisfaction problems, rigorously showing that for such problems a discontinuity of the spine is associated with a 2Ω(n) resolution complexity (and thus a 2Ω(n) complexity of DPLL algorithms) on random instances. The two phenomena have a common underlying cause: the emergence of “large” (linear size) minimally unsatisfiable subformulas of a random formula at the satisfiability phase transition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Spines of random constraint satisfaction problems: definition and connection with computational complexity

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References (43)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-005-7033-2
Publisher site
See Article on Publisher Site

Abstract

We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited connection between the two phenomena indeed exists. Specifically, we extend the definition of the spine order parameter of Bollobás et al. [10] to random constraint satisfaction problems, rigorously showing that for such problems a discontinuity of the spine is associated with a 2Ω(n) resolution complexity (and thus a 2Ω(n) complexity of DPLL algorithms) on random instances. The two phenomena have a common underlying cause: the emergence of “large” (linear size) minimally unsatisfiable subformulas of a random formula at the satisfiability phase transition.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: May 10, 2005

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