Parameterized and Subexponential-Time Complexity of Satisfiability Problems and Applications

Conference paper

DOI: 10.1007/978-3-319-12691-3_48

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8881)
Cite this paper as:
Kanj I., Szeider S. (2014) Parameterized and Subexponential-Time Complexity of Satisfiability Problems and Applications. In: Zhang Z., Wu L., Xu W., Du DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science, vol 8881. Springer, Cham

Abstract

We study the parameterized and the subexponential-time complexity of the weighted and unweighted satisfiability problems on bounded-depth Boolean circuits. We establish relations between the subexponential-time complexity of the weighted and unweighted satisfiability problems, and use them to derive relations among the subexponential-time complexity of several \(\text {NP}\)-hard problem. For instance, we show that the weighted monotone satisfiability problem is solvable in subexponential time if and only if CNF-Sat is. The aforementioned result implies, via standard reductions, that several \(\text {NP}\)-hard problems are solvable in subexponential time if and only if CNF-Sat is. We also obtain threshold functions on structural circuit parameters including depth, number of gates, and fan-in, that lead to tight characterizations of the parameterized and the subexponential-time complexity of the circuit problems under consideration. For instance, we show that the weighted satisfiability problem is \(\text {FPT}\) on bounded-depth circuits with \(O(\log {n})\) gates, where \(n\) is the number of variables in the circuit, and is not \(\text {FPT}\) on bounded-depth circuits of \(\omega (\log {n})\) gates unless the Exponential Time Hypothesis (ETH) fails.

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of ComputingDePaul UniversityChicagoUSA
  2. 2.Vienna University of TechnologyViennaAustria

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