相关论文: Random MAX SAT, Random MAX CUT, and Their Phase Tr…

In this work we propose and analyze a simple randomized algorithm to find a satisfiable assignment for a Boolean formula in conjunctive normal form (CNF) having at most 3 literals in every clause. Given a k-CNF formula phi on n variables,…

We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >=…

We describe an algorithm to solve the problem of Boolean CNF-Satisfiability when the input formula is chosen randomly. We build upon the algorithms of Sch{\"{o}}ning 1999 and Dantsin et al.~in 2002. The Sch{\"{o}}ning algorithm works by…

We consider the fundamental problem of selecting $k$ out of $n$ random variables in a way that the expected highest or second-highest value is maximized. This question captures several applications where we have uncertainty about the…

We derive an upper bound on the number of models for exact satisfiability (XSAT) of arbitrary CNF formulas F. The bound can be calculated solely from the distribution of positive and negated literals in the formula. For certain subsets of…

We study random instances of the weighted $d$-CNF satisfiability problem (WEIGHTED $d$-SAT), a generic W[1]-complete problem. A random instance of the problem consists of a fixed parameter $k$ and a random $d$-CNF formula $\weicnf{n}{p}{k,…

A 3-SAT problem is called positive and planar if all the literals are positive and the clause-variable incidence graph (i.e., SAT graph) is planar. The NAE 3-SAT and 1-in-3-SAT are two variants of 3-SAT that remain NP-complete even when…

Many optimization problems can be cast into the maximum satisfiability (MAX-SAT) form, and many solvers have been developed for tackling such problems. To evaluate a MAX-SAT solver, it is convenient to generate hard MAX-SAT instances with…

Learning-augmented algorithms are a prominent recent development in beyond worst-case analysis. In this framework, a problem instance is provided with a prediction (``advice'') from a machine-learning oracle, which provides partial…

The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on `almost' planar graphs: Given an…

We introduce a diversified top-k partial MaxSAT problem, a combination of partial MaxSAT problem and enumeration problem. Given a partial MaxSAT formula F and a positive integer k, the diversified top-k partial MaxSAT is to find k maximal…

The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…

Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…

The XOR-satisfiability (XORSAT) problem requires finding an assignment of $n$ Boolean variables that satisfy $m$ exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We consider random XORSAT instances,…

Maximum Satisfiability (MaxSAT) is a well-known optimization pro- blem, with several practical applications. The most widely known MAXS AT algorithms are ineffective at solving hard problems instances from practical application domains.…

The $k$-SAT problem for \L{}-clausal forms has been found to be NP-complete if $k\geq 3$. Similar to Boolean CNF formulas, \L{}-clausal forms are important from a theoretical and practical points of view for their expressive power,…

Since the early 2000s physicists have developed an ingenious but non-rigorous formalism called the cavity method to put forward precise conjectures on phase transitions in random problems [Mezard, Parisi, Zecchina: Science 2002]. The cavity…

We study random subgraphs of the $n$-cube $\{0,1\}^n$, where nearest-neighbor edges are occupied with probability $p$. Let $p_c(n)$ be the value of $p$ for which the expected cluster size of a fixed vertex attains the value $\lambda…

We study the behavior of ASAT, a heuristic for solving satisfiability problems by stochastic local search near the SAT/UNSAT transition. The heuristic is focused, i.e. only variables in unsatisfied clauses are updated in each step, and is…

We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. The…