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28
Algorithms for ConstraintSatisfaction Problems: A Survey
, 1992
"... A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraintsatisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, an ..."
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Cited by 447 (0 self)
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A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraintsatisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This article overviews many of these approaches in a tutorial fashion.
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . 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, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 145 (3 self)
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. 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, computeraided 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...
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
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Cited by 130 (1 self)
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. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
A Discrete LagrangianBased GlobalSearch Method for Solving Satisfiability Problems
 Journal of Global Optimization
, 1998
"... Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a n ..."
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Cited by 66 (7 self)
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Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrangemultiplierbased globalsearch method for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, show that equilibrium is reached when a feasible assignment to the original problem is found, and present heuristic algorithms to look for equilibrium points. Instead of restarting from a new starting point when a search reaches a local trap, the Lagrange multipliers in our method provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. One of the major advantages of our method is that it has very few algorithmic parameters to be tuned by users, and the se...
Local Search for Satisfiability (SAT) Problem
, 1993
"... The satisfiability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satisfiability problem play an important role in the development of computing theory and systems. Traditional methods treat the SAT p ..."
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Cited by 38 (4 self)
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The satisfiability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satisfiability problem play an important role in the development of computing theory and systems. Traditional methods treat the SAT problem as a constrained decision problem. During past research, the number of unsatisfiable clauses as the value of an objective function was formulated. This transforms the SAT problem into a search problem  an unconstrained optimization problem to the objective function. A variety of iterative optimization techniques can be used to solve this optimization problem. In this paper, we show how to use local search techniques to solve the SAT problem. The average time complexity analysis and numerous real algorithm executions were performed. They indicate that the local search algorithms are much more efficient than the existing SAT algorithms for certain classes of conjunctive normal form (...
Discrete LagrangianBased Search for Solving MAXSAT Problems
 In Proc. Int'l Joint Conf. on Artificial Intelligence
, 1997
"... Weighted maximum satisfiability problems (MAXSAT) are difficult to solve due to the large number of local minima in their search space. In this paper we propose a new discrete Lagrangian based search method (DLM) for solving these problems. Instead of restarting from a new point when the search rea ..."
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Cited by 33 (5 self)
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Weighted maximum satisfiability problems (MAXSAT) are difficult to solve due to the large number of local minima in their search space. In this paper we propose a new discrete Lagrangian based search method (DLM) for solving these problems. Instead of restarting from a new point when the search reaches a local minimum, the Lagrange multipliers in DLM provide a force to lead the search out of the local minimum and move it in a direction provided by the multipliers. Since DLM has very few parameters to be tuned, it can be made deterministic and the results, reproducible. We compare DLM with GRASP in solving a large set of test problems, and show that it finds better solutions and is substantially faster. DLM has a solid theoretical foundation that can be used as a systematic approach for solving general discrete optimization problems. 1 Introduction The satisfiability (SAT) problem is defined as follows. Given a set of n clauses fC 1 , C 2 , \Delta \Delta \Delta, Cn g on m variables x...
Efficient Local Search with Conflict Minimization: A Case Study of the NQueens Problem
 IEEE Transactions on Knowledge and Data Engineering
, 1994
"... Backtracking search is frequently applied to solve a constraintbased 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 ..."
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Cited by 31 (6 self)
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Backtracking search is frequently applied to solve a constraintbased 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 constraintbased search problem, the nqueens problem. An efficient local search algorithm for the nqueens 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 nqueens 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, nqueens 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 ...
Reactive Search, a historybased heuristic for MAXSAT
 ACM Journal of Experimental Algorithmics
, 1996
"... The Reactive Search (RS) method proposes the integration of a simple historybased feedback scheme into local search for the online determination of free parameters. In this paper a new RS algorithm is proposed for the approximated solution of the Maximum Satisfiability problem: a component base ..."
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Cited by 28 (1 self)
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The Reactive Search (RS) method proposes the integration of a simple historybased feedback scheme into local search for the online determination of free parameters. In this paper a new RS algorithm is proposed for the approximated solution of the Maximum Satisfiability problem: a component based on local search with temporary prohibitions is complemented with a reactive scheme that determines ("learns") the appropriate value of the prohibition parameter by monitoring the Hamming distance along the search trajectory (algorithm HRTS). In addition, the nonoblivious functions recently introduced in the framework of approximation algorithms are used to discover a better local optimum in the initial part of the search.
Global Optimization for Satisfiability (SAT) Problem
, 1994
"... The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT ..."
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Cited by 22 (3 self)
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The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT problem on Boolean space f0; 1g m into an unconstrained global optimization problem on real space E m . A direct correspondence between the solution of the SAT problem and the global minimum point of the UniSAT objective function is established. Many existing global optimization algorithms can be used to solve the UniSAT problems. Combined with backtracking /resolution procedures, a global optimization algorithm is able to verify satisfiability as well as unsatisfiability. This approach achieves significant performance improvements for certain classes of conjunctive normal form (CNF ) formulas. It offers a complementary approach to the existing SAT algorithms.
Postprocessing decision trees to extract actionable knowledge
 In ICDM
, 2003
"... Most data mining algorithms and tools stop at discovered customer models, producing distribution information on customer profiles. Such techniques, when applied to industrial problems such as customer relationship management (CRM), are useful in pointing out customers who are likely attritors and cu ..."
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Cited by 19 (2 self)
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Most data mining algorithms and tools stop at discovered customer models, producing distribution information on customer profiles. Such techniques, when applied to industrial problems such as customer relationship management (CRM), are useful in pointing out customers who are likely attritors and customers who are loyal, but they require human experts to postprocess the mined information manually. Most of the postprocessing techniques have been limited to producing visualization results and interestingness ranking, but they do not directly suggest actions that would lead to an increase the objective function such as profit. In this paper, we present a novel algorithm that suggest actions to change customers from an undesired status (such as attritors) to a desired one (such as loyal) while maximizing objective function: the expected net profit. We develop these algorithms under resource constraints that are abound in reality. The contribution of the work is in taking the output from an existing mature technique (decision trees, for example), and producing novel, actionable knowledge through automatic postprocessing. 1.