Related papers: Complexity of several constraint satisfaction prob…
This work presents two new algorithms for performing constraint satisfaction. The first algorithm presented, DMaxWalkSat, is a constraint solver specialized for solving dynamic, weighted constraint satisfaction problems. The second…
Local search algorithms are well-known methods for solving large, hard instances of the satisfiability problem (SAT). The performance of these algorithms crucially depends on heuristics for setting noise parameters and scoring variables.…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
We introduce and benchmark a stochastic local search heuristic for the NP-complete satisfiability problem 3-SAT that drastically outperforms existing solvers in the notoriously difficult realm of critically hard instances. Our construction…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
We study the performances of stochastic heuristic search algorithms on Uniquely Extendible Constraint Satisfaction Problems with random inputs. We show that, for any heuristic preserving the Poissonian nature of the underlying instance, the…
Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if…
In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free…
Stochastic local search (SLS) algorithms have exhibited great effectiveness in finding models of random instances of the Boolean satisfiability problem (SAT). As one of the most widely known and used SLS algorithm, WalkSAT plays a key role…
To test incomplete search algorithms for constraint satisfaction problems such as 3-SAT, we need a source of hard, but satisfiable, benchmark instances. A simple way to do this is to choose a random truth assignment A, and then choose…
Satisfiability problem (SAT) is a cornerstone of computational complexity with broad industrial applications, and it remains challenging to optimize modern SAT solvers in real-world settings due to their intricate architectures. While…
In this paper, we provide a deterministic polynomial time algorithm that determines satisfiability of 3-SAT. The complexity analysis for the algorithm takes into account no efficiency and yet provides a low enough bound, that efficient…