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On forward checking for non-binary constraint satisfaction

2002
*
Artificial Intelligence
*

Solving

doi:10.1016/s0004-3702(02)00263-1
fatcat:k573hdzuvzbf7jzbstvgycmtbq
*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. ...##
###
On Forward Checking for Non-binary Constraint Satisfaction
[chapter]

1999
*
Lecture Notes in Computer Science
*

Solving

doi:10.1007/978-3-540-48085-3_7
fatcat:scgnwa2l6nh6nlypbvymy7h4ya
*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. ...##
###
Decomposable Constraints
[chapter]

2000
*
Lecture Notes in Computer Science
*

We present many new results about the level of consistency achieved by the

doi:10.1007/3-540-44654-0_7
fatcat:vhx47bm7e5egheubxcknqbubz4
*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. ...##
###
Decomposable constraints☆☆Supported by EPSRC award GR/L/24014. The authors wish to thank other members of the APES research group

2000
*
Artificial Intelligence
*

We present many results about the level of consistency achieved by the

doi:10.1016/s0004-3702(00)00051-5
fatcat:ws5ugkrhyvaahll7nmdgc6vt5e
*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. ...##
###
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 ...

##
###
On Algorithms for Decomposable Constraints
[chapter]

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 ...

##
###
Non-binary Constraints
[chapter]

1999
*
Lecture Notes in Computer Science
*

Since the origins of the

doi:10.1007/978-3-540-48085-3_2
fatcat:nx76mxie6rbevbrqypfedr5t7u
*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*. ...##
###
Constraint Satisfaction by Means of Dynamic Polyhedra
[chapter]

2002
*
Operations Research Proceedings 2001
*

In this paper, we propose an algorithm called "HSA≠" that solves

doi:10.1007/978-3-642-50282-8_50
fatcat:gsuru7b2xzewpph4orx5y7tzky
*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 ...##
###
Greater Efficiency for Conditional Constraint Satisfaction
[chapter]

2003
*
Lecture Notes in Computer Science
*

The advanced algorithms extend

doi:10.1007/978-3-540-45193-8_44
fatcat:cobbed2km5ghznpnlfadptjtza
*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] . ...##
###
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]

2002
*
Lecture Notes in Computer Science
*

Nowadays, many researchers are working

doi:10.1007/3-540-36079-4_14
fatcat:hgs3n6m7fbc7tdq274vuagdazq
*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 ...##
###
NOGOOD RECORDING FOR STATIC AND DYNAMIC CONSTRAINT SATISFACTION PROBLEMS

1994
*
International journal on artificial intelligence tools
*

Many AI synthesis problems such as planning, scheduling or design may be encoded in a

doi:10.1142/s0218213094000108
fatcat:7baegxaqrre2xmww6tac4yvhzm
*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 ...##
###
An Incremental and Non-binary CSP Solver: The Hyperpolyhedron Search Algorithm
[chapter]

2001
*
Lecture Notes in Computer Science
*

It carries out the search through a hyperpolyhedron that maintains those solutions that satisfy all metric

doi:10.1007/3-540-45578-7_79
fatcat:w4upny6775c2vnr4accr5pouye
*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. ...##
###
A non-binary constraint ordering heuristic for constraint satisfaction problems

2008
*
Applied Mathematics and Computation
*

Furthermore, the order in which

doi:10.1016/j.amc.2007.08.064
fatcat:qt4m5azu3vdmlpurspzgccfuxm
*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*...##
###
Solving Non-binary CSPs Using the Hidden Variable Encoding
[chapter]

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 ...

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