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26
A Generic ArcConsistency Algorithm and its Specializations
 Artificial Intelligence
, 1992
"... Consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arcconsistency algorithms have been proposed, originating from Waltz's filtering algorithm [26] and culminating in the optimal algorithm AC4 of Mohr ..."
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Cited by 192 (7 self)
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Consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arcconsistency algorithms have been proposed, originating from Waltz's filtering algorithm [26] and culminating in the optimal algorithm AC4 of Mohr and Henderson [15]. AC4 runs in O(ed 2 ) in the worst case, where e is the number of arcs (or constraints) and d is the size of the largest domain. Being applicable to the whole class of (binary) CSP, these algorithms do not take into account the semantics of constraints. In this paper, we present a new generic arcconsistency algorithm AC5. This algorithm is parametrized on two specified procedures and can be instantiated to reduce to AC3 and AC4. More important, AC5 can be instantiated to produce an O(ed) algorithm for a number of important classes of constraints: functional, antifunctional, monotonic and their generalization to (functional, antifunctional, and monotonic) piecewise constraints. We also show that AC5 has an important application in constraint logic programming over finite domains [23]. The kernel of the constraint solver for such a programming language is an arcconsistency algorithm for a set of basic constraints. We prove that AC5, in conjunction with node consistency, provides a decision procedure for these constraints running in time O(ed).
Reasoning about Qualitative Temporal Information
 Artificial Intelligence
, 1992
"... Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An intervalbased framework and a pointbased framework have been proposed for representing such temporal information. In this paper, we address ..."
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Cited by 137 (6 self)
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Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An intervalbased framework and a pointbased framework have been proposed for representing such temporal information. In this paper, we address two fundamental reasoning tasks that arise in applications of these frameworks: Given possibly indefinite and incomplete knowledge of the relationships between some intervals or points, (i) find a scenario that is consistent with the information provided, and (ii) find the feasible relations between all pairs of intervals or points. For the pointbased framework and a restricted version of the intervalbased framework, we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations. Our algorithms are marked improvements over the previously known algorithms. In particular, we develop an O(n 2 ) time algorithm for finding one co...
A Theoretical Evaluation of Selected Backtracking Algorithms
 Artificial Intelligence
, 1997
"... In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a di erent, purely theoretical approach, which is based on charact ..."
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Cited by 115 (3 self)
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In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a di erent, purely theoretical approach, which is based on characterizations of the sets of search treenodes visited by the backtracking algorithms. A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such wellknown concepts as backtrack, backjump, and domain annihilation. The characterizations enable us to: (a) prove the correctness of the algorithms, and (b) partially order the algorithms according to two standard performance measures: the number of nodes visited, and the number of consistency checks performed. Among other results, we prove the correctness of Backjumping and Con ictDirected Backjumping, and show that Forward Checking never visits more nodes than Backjumping. Our approach leads us also to propose a modi cation to two hybrid backtracking algorithms, Backmarking with Backjumping (BMJ) and Backmarking with Con ictDirected Backjumping (BMCBJ), so that they always perform fewer consistency checks than the original algorithms. 1
Recent Advances in AI Planning
 AI MAGAZINE
, 1999
"... The past five years have seen dramatic advances in planning algorithms, with an emphasis on propositional methods such as Graphplan and compilers that convert planning problems into propositional CNF formulae for solution via systematic or stochastic SAT methods. Related work on the Deep Space O ..."
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Cited by 108 (0 self)
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The past five years have seen dramatic advances in planning algorithms, with an emphasis on propositional methods such as Graphplan and compilers that convert planning problems into propositional CNF formulae for solution via systematic or stochastic SAT methods. Related work on the Deep Space One spacecraft control algorithms advances our understanding of interleaved planning and execution. In this survey,we explain the latest techniques and suggest areas for future research.
A rearrangement search strategy for determining propositional satisfiability
 in Proceedings of the National Conference on Artificial Intelligence
, 1988
"... We present a simple algorithm for determining the satis ability of propositional formulas in Conjunctive Normal Form. As the procedure searches for a satisfying truth assignment it dynamically rearranges the order in which variables are considered. The choice of which variable to assign a truth valu ..."
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Cited by 74 (1 self)
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We present a simple algorithm for determining the satis ability of propositional formulas in Conjunctive Normal Form. As the procedure searches for a satisfying truth assignment it dynamically rearranges the order in which variables are considered. The choice of which variable to assign a truth value next is guided by an upper bound on the size of the search remaining � the procedure makes the choice which yields the smallest upper bound on the size of the remaining search. We describe several upper bound functions and discuss the tradeo between accurate upper bound functions and the overhead required to compute the upper bounds. Experimental data shows that for one easily computed upper bound the reduction in the size of the search space more than compensates for the overhead involved in selecting the next variable. 1
Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORDHorn Class
 Constraints
, 1997
"... While the worstcase computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. ..."
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Cited by 59 (6 self)
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While the worstcase computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. In this paper, we will demonstrate that using the ORDHorn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm is complete when using the ORDHorn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORDHorn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm. Contents 1 Introduction 1 2 Allen's...
Resolution versus Search: Two Strategies for SAT
 Journal of Automated Reasoning
, 2000
"... The paper compares two popular strategies for solving propositional satisfiability, backtracking search and resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the "width" (w) of the problem's graph. ..."
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Cited by 51 (1 self)
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The paper compares two popular strategies for solving propositional satisfiability, backtracking search and resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the "width" (w) of the problem's graph.
A Computational Study of Constraint Satisfaction for Multiple Capacitated Job Shop Scheduling
 European Journal of Operational Research
, 1996
"... Weintroduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously.We presentan algorithm based on constraint satisfaction techniques to handle the problem e#ectively. The ..."
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Cited by 38 (4 self)
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Weintroduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously.We presentan algorithm based on constraint satisfaction techniques to handle the problem e#ectively. The most importantnovel feature of our algorithm is the consistency checking. An empirical performance analysis is performed using a wellknown set of instances of the job shop scheduling problem and a newly constructed set of instances of the multiple capacitated job shop scheduling problem. We show that our algorithm performs well for both sets of instances.
From Restricted Path Consistency to MaxRestricted Path Consistency
 PROCEEDINGS OF THIRD INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING (CP97
, 1997
"... There is no need to show the importance of the filtering techniques to solve constraint satisfaction problems i.e. to find values for problem variables subject to constraints that specify whichcombinations of values are consistent. They can be used during a preprocessingstep to remove once and for a ..."
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Cited by 35 (11 self)
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There is no need to show the importance of the filtering techniques to solve constraint satisfaction problems i.e. to find values for problem variables subject to constraints that specify whichcombinations of values are consistent. They can be used during a preprocessingstep to remove once and for all some local inconsistencies, or duringthesearch toefficiently prunethe search tree. Recently, in [5], a comparison of the most practicable filteringtechniques concludes that restricted pathconsistency (RPC) is a promising local consistency that requires little additional cpu time compared to arc consistency while removing most of thepathinverse inconsistentvalues. However, the RPC algorithm used for this comparison (presented in [1] and called RPC1 in the following) has a non optimal worst case time complexity and bad average timeand space complexities. Therefore, we propose RPC2, a new RPC algorithm with O(end 2 )worst case time complexity and requiring less space than RPC1 in practice. The second aim of this paper is to extend RPC tonew local consistencies, kRPC and MaxRPC, andto compare their pruning efficiency withtheother practicable local consistencies. Furthermore, we propose andstudy a MaxRPC algorithm based on AC6 thatwe used for this comparison.
Intelligent Backtracking Techniques for Job Shop Scheduling
 In Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning
, 1992
"... This paper studies a version of the job shop scheduling problem in which some operations have to be scheduled within nonrelaxable time windows (i.e. earliest/latest possible start time windows). This problem is a wellknown NPcomplete Constraint Satisfaction Problem (CSP). A popular method for solv ..."
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Cited by 33 (4 self)
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This paper studies a version of the job shop scheduling problem in which some operations have to be scheduled within nonrelaxable time windows (i.e. earliest/latest possible start time windows). This problem is a wellknown NPcomplete Constraint Satisfaction Problem (CSP). A popular method for solving these types of problems consists in using depthfirst backtrack search. Our earlier work focused on developing efficient consistency enforcing techniques and efficient variable /value ordering heuristics to improve the efficiency of this procedure. In this paper, we combine these techniques with new lookback schemes that help the search procedure recover from socalled deadend search states (i.e. partial solutions that cannot be completed without violating some constraints). More specifically, we successively describe three intelligent backtracking schemes: Dynamic Consistency Enforcement dynamically enforces higher levels of consistency in selected critical subproblems, Learning From Fa...