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On forward checking for non-binary constraint satisfaction

Christian Bessière, Pedro Meseguer, Eugene C. Freuder, Javier Larrosa
2002 Artificial Intelligence  
Solving non-binary constraint satisfaction problems, a crucial challenge today, can be tackled in two different ways: translating the non-binary problem into an equivalent binary one, or extending binary  ...  This paper focuses on the well-known forward checking algorithm, and shows that it can be generalized to several non-binary versions, all fitting its binary definition.  ...  For other algorithms, such as forward checking (FC) [8] , several generalizations are possible.  ... 
doi:10.1016/s0004-3702(02)00263-1 fatcat:k573hdzuvzbf7jzbstvgycmtbq

On Forward Checking for Non-binary Constraint Satisfaction [chapter]

Christian Bessière, Pedro Meseguer, Eugene C. Freuder, Javier Larrosa
1999 Lecture Notes in Computer Science  
Solving non-binary constraint satisfaction problems, a crucial challenge today, can be tackled in two different ways: translating the non-binary problem into an equivalent binary one, or extending binary  ...  This paper focuses on the well-known forward checking algorithm, and shows that it can be generalized to several non-binary versions, all fitting its binary definition.  ...  For other algorithms, such as forward checking (FC) [8] , several generalizations are possible.  ... 
doi:10.1007/978-3-540-48085-3_7 fatcat:scgnwa2l6nh6nlypbvymy7h4ya

Decomposable Constraints [chapter]

Ian Gent, Kostas Stergiou, Toby Walsh
2000 Lecture Notes in Computer Science  
We present many new results about the level of consistency achieved by the forward checking algorithm and its various generalizations to non-binary constraints.  ...  We compare theoretically the levels of consistency which are achieved on non-binary constraints to those achieved on their binary decomposition.  ...  The authors are members of the APES research group (http://www.cs. strath.ac.uk/˜apes) and wish to thank the other members for their comments and feedback.  ... 
doi:10.1007/3-540-44654-0_7 fatcat:vhx47bm7e5egheubxcknqbubz4

Decomposable constraints☆☆Supported by EPSRC award GR/L/24014. The authors wish to thank other members of the APES research group

Ian Gent, Kostas Stergiou, Toby Walsh
2000 Artificial Intelligence  
We present many results about the level of consistency achieved by the forward checking algorithm and its various generalizations to non-binary constraints.  ...  Many constraint satisfaction problems can be naturally and efficiently modelled using non-binary constraints like the "all-different" and "global cardinality" constraints.  ...  For a decomposable non-binary constraint satisfaction problem, the forward checking algorithm FC on the binary decomposition strictly dominates the generalized forward checking algorithm nFC0. Proof.  ... 
doi:10.1016/s0004-3702(00)00051-5 fatcat:ws5ugkrhyvaahll7nmdgc6vt5e

Forthcoming Papers

2002 Artificial Intelligence  
Binary vs. non-binary constraints There are two well known transformations from non-binary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the  ...  Our comparison focuses on two backtracking algorithms that maintain a local consistency property at each node in their search tree: the forward checking and maintaining arc consistency algorithms.  ...  Walsh, Binary vs. non-binary constraints There are two well known transformations from non-binary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains  ... 
doi:10.1016/s0004-3702(02)00281-3 fatcat:6gorcgplazbgtpkw4sdr7oajwa

On Algorithms for Decomposable Constraints [chapter]

Kostas Stergiou
2002 Lecture Notes in Computer Science  
For example, a non-binary all-different constraint can be decomposed into a clique of binary not-equals constraints.  ...  Non-binary constraints are present in many real-world constraint satisfaction problems. Certain classes of these constraints, like the all-different constraint, are "decomposable".  ...  It was proved that for a decomposable non-binary constraint satisfaction problem, the forward checking algorithm FC on the binary decomposition is strictly stronger than the generalized algorithm nFC0  ... 
doi:10.1007/3-540-46014-4_7 fatcat:eq4fxbtg7rbkthgkrgza52z4om

Non-binary Constraints [chapter]

Christian Bessière
1999 Lecture Notes in Computer Science  
Since the origins of the constraint satisfaction paradigm, its restriction to binary constraints has concentrated a significant part of the work.  ...  This is understandable because new ideas/techniques are usually much simpler to present/ elaborate by first restricting them to the binary case.  ...  Dealing with non-binary constraints for real-world problems raises questions that do not appear as crucial on binary constraints.  ... 
doi:10.1007/978-3-540-48085-3_2 fatcat:nx76mxie6rbevbrqypfedr5t7u

Constraint Satisfaction by Means of Dynamic Polyhedra [chapter]

Miguel A. Salido, Adriana Giret, Federico Barber
2002 Operations Research Proceedings 2001  
In this paper, we propose an algorithm called "HSA≠" that solves non-binary constraint satisfaction problems in a natural way as an incremental and non-binary CSP solver.  ...  It is well known that any non-binary CSP can be transformed into an equivalent binary one, using some of the current techniques.  ...  The basic reasons were the simplicity of dealing with binary constraints compared to non-binary ones and the fact that any non-binary constraint satisfaction problem can be transformed into an equivalent  ... 
doi:10.1007/978-3-642-50282-8_50 fatcat:gsuru7b2xzewpph4orx5y7tzky

Greater Efficiency for Conditional Constraint Satisfaction [chapter]

Mihaela Sabin, Eugene C. Freuder, Richard J. Wallace
2003 Lecture Notes in Computer Science  
The advanced algorithms extend forward checking and maintaining arc consistency to CCSPs.  ...  A conditional constraint satisfaction problem (CCSP) extends a standard constraint satisfaction problem (CPS) with a conditionbased component that controls what variables participate in problem solutions  ...  We want to generalize the current implementations of CondFC and CondMAC to handle non-binary constraints and take advantage of efficient non-binary local consistency algorithms [19, 22, 23] .  ... 
doi:10.1007/978-3-540-45193-8_44 fatcat:cobbed2km5ghznpnlfadptjtza

Page 7844 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
(IRL-CORK-CCC; Cork); Larrosa, Javier (E-UPB-LI; Barcelona) On forward checking for non-binary constraint satisfaction. (English summary) Artificial Intelligence 141 (2002), no. 1-2, 205-224.  ...  This paper focuses on the well-known forward checking algorithm and shows that it can be generalized to several non-binary versions, all fitting its binary definition.  ... 

Disjunction of Non-binary and Numeric Constraint Satisfaction Problems [chapter]

Miguel A. Salido, Federico Barber
2002 Lecture Notes in Computer Science  
Nowadays, many researchers are working on Constraint Satisfaction Problems (CSPs).  ...  However, this transformation may be an inadequate or inefficient way to manage certain types of non-binary constraints.  ...  The basic reasons are the simplicity of dealing with binary constraints compared to nonbinary ones and the fact that any non-binary constraint satisfaction problem can be transformed into an equivalent  ... 
doi:10.1007/3-540-36079-4_14 fatcat:hgs3n6m7fbc7tdq274vuagdazq

NOGOOD RECORDING FOR STATIC AND DYNAMIC CONSTRAINT SATISFACTION PROBLEMS

THOMAS SCHIEX, GÉRARD VERFAILLIE
1994 International journal on artificial intelligence tools  
Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problems (CSP).  ...  We first introduce the principles used for nogood generation and then examine various recording schemes, on top of different tree search algorithms, characterizing the tradeoffs between the amount of recorded  ...  The functions forward-check and un-forward are introduced. forward-check achieves forward-checking and also store, each time a domain is reduced, the constraint that reduced the domain as a value-killer  ... 
doi:10.1142/s0218213094000108 fatcat:7baegxaqrre2xmww6tac4yvhzm

An Incremental and Non-binary CSP Solver: The Hyperpolyhedron Search Algorithm [chapter]

Miguel A. Salido, Federico Barber
2001 Lecture Notes in Computer Science  
It carries out the search through a hyperpolyhedron that maintains those solutions that satisfy all metric non-binary temporal constraints.  ...  Constraint programming is gaining a great deal of attention because many combinatorial problems especially in areas of planning and scheduling can be expressed in a natural way as a Constraint Satisfaction  ...  For each constraint (step 2), the consistency check cost depends linearly on the number of hyperpolyhedron vertices, but not on the variable domains.  ... 
doi:10.1007/3-540-45578-7_79 fatcat:w4upny6775c2vnr4accr5pouye

A non-binary constraint ordering heuristic for constraint satisfaction problems

Miguel A. Salido
2008 Applied Mathematics and Computation  
Furthermore, the order in which constraints are studied can improve efficiency, particularly in problems with non-binary constraints.  ...  tightest ones are studied first.  ...  In spite of the additivity of constraints, only a few works have be done on binary constraint ordering mainly for arc-consistency algorithms [25, 16, 10] , but little work has be done on non-binary constraint  ... 
doi:10.1016/j.amc.2007.08.064 fatcat:qt4m5azu3vdmlpurspzgccfuxm

Solving Non-binary CSPs Using the Hidden Variable Encoding [chapter]

Nikos Mamoulis, Kostas Stergiou
2001 Lecture Notes in Computer Science  
Non-binary constraint satisfaction problems (CSPs) can be solved in two different ways.  ...  Empirical results on various implementations of such algorithms reveal that the hidden variable is competitive and in many cases better than the non-binary representation for certain classes of non-binary  ...  We also show that, like MGAC, the generalizations of forward checking to non-binary CSPs can be simulated by a corresponding binary forward checking algorithm on the hidden variable encoding that only  ... 
doi:10.1007/3-540-45578-7_12 fatcat:naqtxx7q2bbefosko2bmnsuq4e
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