Thomas Bläsius, Tobias Friedrich, Andreas Göbel, Jordi Levy, Ralf Rothenberger
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引用次数: 1
Abstract
Abstract Satisfiability is considered the canonical NP‐complete problem and is used as a starting point for hardness reductions in theory, while in practice heuristic SAT solving algorithms can solve large‐scale industrial SAT instances very efficiently. This disparity between theory and practice is believed to be a result of inherent properties of industrial SAT instances that make them tractable. Two characteristic properties seem to be prevalent in the majority of real‐world SAT instances, heterogeneous degree distribution and locality. To understand the impact of these two properties on SAT, we study the proof complexity of random ‐SAT models that allow to control heterogeneity and locality. Our findings show that heterogeneity alone does not make SAT easy as heterogeneous random ‐SAT instances have superpolynomial resolution size. This implies intractability of these instances for modern SAT‐solvers. In contrast, modeling locality with underlying geometry leads to small unsatisfiable subformulas, which can be found within polynomial time.
期刊介绍:
It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness.
Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.