. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

Backtracking search is frequently applied to solve a constraint-based search problem but it often suffers from exponential growth of computing time. We present an alternative to backtracking search: local search based on conflict minimization. We have applied this general search framework to study a benchmark constraint-based search problem, the n-queens problem. An efficient local search algorithm for the n-queens problem was implemented. This algorithm, running in linear time, does not backtrack at all. It is capable of finding a solution for extremely large size n-queens problems. For example, on a workstation computer, it can find a solution for 3,000,000 queens in less than 55 seconds. Keywords: conflict minimization, local search, n-queens problem, nonbacktracking search. 1 This research has been supported in part by the University of Utah research fellowships, in part by the Research Council of Slovenia, and in part by ACM/IEEE academic scholarship awards. 1 Introduction A ...

The n-queens problem, originally introduced in 1850 by Carl Gauss, may be stated as follows: find a placement of n queens on an n×n chessboard, such that no one queen can be taken by any other. While it has been well known that the solution to the n-queens problem is n, numerous solutions have been published since the original problem was proposed. Many of these solutions rely on providing a specific formula for placing queens or transposing smaller solutions sets to provide solutions for larger values of n (Bernhardsson, 1991 and Hoffman et al., 1969). Empirical observations of smaller-size problems show that the number of solutions increases exponentially with increasing n (Sosi and Gu, 1994). Alternatively, search-based algorithms have been