A Multistage View on 2-Satisfiability

From Hall's Marriage Theorem to Boolean Satisfiability and Back

Motivated by the application of Hall's Marriage Theorem in various LP-rounding problems, we introduce a generalization of the classical marriage problem (CMP) that we call the Fractional Marriage Problem. We show that the Fractional Marriage Problem is NP-Complete by reduction from Boolean Satisfiability (SAT). We show that when we view the classical marriage problem (a.k.a. bipartite matching) as a sub-class of SAT we get a new class of polynomial-time satisfiable SAT instances that we call CMP-SAT, different from the classically known polynomial-time satisfiable SAT instances 2-SAT, Horn-SAT…

An alternate view of complexity in k-SAT problems

The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large system limit. Two different approaches to obtaining this threshold have been discussed in the literature - using first or second-moment methods which give rigorous bounds or using the non-rigorous but powerful replica-symmetry breaking (RSB) approach, which gives very accurate predictions on random graphs. In this paper, we lay out a different route to obtainin…

A New Look at Survey Propagation and its Generalizations

This paper provides a new conceptual perspective on survey propagation, which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k-SAT problems even with densities close to the satisfiability threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number ρ\in [0,1]. We then show that applying belief propagation--a well-known ``message-passing'' technique for estimating marginal probabilities--to this family of MRFs recovers a known fami…

线性平面3-SAT及其在规划中的应用

Linear Planar 3-SAT and Its Applications in Planning

本文定义并证明了结合线性与平面特征的Linear Planar 3-SAT的NP完全性及其重构问题的PSPACE完全性，并将结果应用于证明两类多智能体路径规划问题的复杂度。