Choueiry, B., and Noubir, G. 1998. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In Proc. of AAAI-98, 326--333.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....problems a valuable class of problems for CBR adaptation methods. Solutions which can be shown to apply to CSP type problems can be applied to a wide range of problems. This paper presents a method based on the concepts of interchangeability [9] and neighbourhood partial interchangeability (NPI) [10]. These methods can be used to capture equivalence among values of a variable in a discrete CSP (original interchangeabil ity) and localise the effect of modifications to some variables and determine relations between close solutions. These techniques are applied and extended to case adaptation ....

....can be generated by modifying the values of the indicated variables only. Again, there is no efficient algorithm for computing PI set. A localised algorithm has however been proposed for computing Neighbourhood Partial Interchangeability (NPI) sets of variables with the corresponding NPI values [10]. Definition 5 (Neighbourhood Partial Interchangeability NPI) Values V i = a and V i = b are neighbourhood partial interchangeable (NPI) with respect to a set of variables S if for every constraint between V i and the neighbourhood of set S, for every tuple that admits V i = a there is ....

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B. Y. Choueiry and G. Noubir. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In Proc. of AAAI-98, pages 326--333, Madison, Wiscowsin, 1998.

....us a first solution and it is easy to test whether changing an interchangeable value gives us another solution. To identify neighbourhood interchangeable values we can construct discrimination trees. The leaves of the trees will be the equivalence classes of neighbourhood interchangeable values [6]. The adaptation model for a case thus consists of all variables which the customer might have to change, plus the interchangeabilities which are applicable to the case and define what can be changed. X X 1 2 Fig. 3. Graphic representation of two dimensional discrete space We take as the ....

....In fact, the number of possibilities grows exponentially with the size of the considered sets, and a general search is clearly unmanageable. A variable V affects the problem through the constraints that link V to other variables in the problem, thus through V s neighbourhood N(V) As observed in [6], if V is partially interchangeable with respect to S, then S must include at least one node of N(V) Thus, it makes sense to compute partial interchangeability by considering increasingly large neighbourhoods of V. 3] gives an efficient algorithm for computing neighbourhood interchangeabilities ....

Berthe Y. Choueiry and Guevara Noubir. On the computation of local interchangeability in discrete constraint satisfaction problems. In Proc. of AAAI-98, pages 326--333, Madison, Wiscowsin, 1998.

....of a variable in a discrete constraint satisfaction problem. Value v = a is substitutable for v = b if for any solution where v = a, there is an identical solution except that v = b. Values v = a and v = b are interchangeable if they are substitutable both ways. Fig. 2 shows a CSP (taken from [21]) that illustrates interchangeability. PSfrag replacements v1 v2 v3 d b, d b, c c, d, e, f #= #= #= Fig. 2: An example of CSP with interchangeable values. Full Interchangeability considers all constraints in the problem and checks if a values a and b for a certain variable v ....

Choueiry, B.Y., Noubir, G.: On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In: Proc. of AAAI-98, Madison, Wiscowsin (1998) 326--333

....of a variable in a discrete constraint satisfaction problem. Value v = a is substitutable for v = b if for any solution where v = a, there is an identical solution except that v = b. Values v = a and v = b are interchangeable if they are substitutable both ways. Fig. 2 shows a CSP (taken from [15]) that illustrates interchangeability. Full Interchangeability considers all constraints in the problem and checks if a values a and b for a certain variable v can be interchanged without a#ecting the global solution. In the CSP in Fig. 2, d, e and f are fully interchangeable for v 4 . This is ....

Choueiry, B.Y., Noubir, G.: On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In: Proc. of AAAI-98, Madison, Wiscowsin (1998) 326--333

.... Freuder provided also an algorithm for computing local interchangeability, which further proved to be an efficient technique for preprocessing prior to further search CSP solutions [3] Further, the procedure for computing local interchangeability proposed by Freuder was extended by Choueiry [4] for a weaker interchangeability form: neighbourhood partial interchangeability. In spite of its importance for many fields (like configuration [1] diagnosis [5] scheduling [6] planning [7] robot control [8] and the challenge its poses for the development of theoretical new approach to ....

....nor practical tested. 2 Related Work Contempt to its importance, interchangeability has received little attention in contrast to backtracking and consistency filtering. Besides we review the contributions on this topic and the relations among them as they were described by Choueiry and Noubir in [4]. Figure 1 summarise these relations. In [2] Freuder introduces the concept of interchangeability and defines various kinds of value interchangeability: Full Interchangeability (FI) K Interchangeability (KI) Neighbourhood Interchangeability (NI) Substitutability (SUB) Partial ....

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Berthe Y. Choueiry and Guevara Noubir. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In Proc. of AAAI-98, pages 326--333, Madison, Wiscowsin, 1998.

....simpler (even simplistic) overall search routine. It would certainly be interesting to combine our work with that on complex local problems, 18] and that on the exchange of aggregates [16] Another body of work with potential relations to clusters is that on interchangeability of values in CSPs [4, 6, 2]: groups of solutions (or locally consistent solutions) that are related by interchange of values of values for variables. It would be interesting to see whether interchanges (or symmetries) could be used to generate some forms of clusters, and whether the cluster methods might help to detect ....

Berthe Y. Choueiry and Gouvera Noubir. On the computation of local interchangeability in discrete constraint satisfaction problems. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI--98), pages 326--333, 1998.

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B. Y. Choueiry and G. Noubir. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. AAAI-98, pages 326-333, 1998.

....value for the variable taken from the same domain bundle without altering the assignments of the remaining variables. Since the strategy devised by Haselbock computes domain partitions in a pre processing step prior to search, we call this strategy static bundling and denote it NIC FC. We proposed [7] a weak form of NI, namely neighborhood partial interchangeability (NPI) that can be controlled to compute interchangeability anywhere between, and including, NI and NIC , see Fig. 1. In [1, 2] we proposed to recompute NPI relations dynamically during NI NPI [Haselboeck 93] Freuder 91] Choueiry ....

Berthe Y. Choueiry and Guevara Noubir. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. Technical Report KSL98 -24, Knowledge Systems Laboratory, Department of Computer Science, Stanford University, Stanford, CA, 1998. Preliminary version in Proc. of AAAI'98.

..... Below we summarize our previous results [5, 2, 4] which motivate the investigations we report here. In [5] we proposed to compute interchangeability dynamically during search using a generalized form of Freuder s discrimination tree, the joint discrimination tree of Choueiry and Noubir [6]. We called this type of interchangeability dynamic neighborhood partial interchangeability (DNPI) Since DNPI is computed during search, we say that it performs dynamic bundling. DNPI induces less domain fragmentation (larger partitions) than NIC and is thus likely to find larger solution ....

Berthe Y. Choueiry and Guevara Noubir. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In Proc. of AAAI98, pages 326--333, Madison, Wisconsin, 1998. Revised version KSL-98-24, http://ksl-web.stanford.edu/KSL Abstracts/KSL-98-24.html.

....6 ] for computing a strong type of local interchangeability. In the rest of the paper we describe our contributions. In Section 3.1, we extend the above mentioned procedure; we show Technical report KSL 98 24. October 2, 1998. A previous version of this paper appeared in the proceedings of AAAI 98 [ 5 ] . that this extension enables the computation of a weak form of interchangeability (Section 3.2) as well as the identification of locally independent subproblems (Section 3.3) then we describe how these interchangeable sets are organized in a hierarchy (Section 3.4) Further, we sketch how to ....

Berthe Y. Choueiry and Guevara Noubir. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In Proc. of AAAI-98, pages 326--333, Madison, Wisconsin, 1998.

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Choueiry, B., and Noubir, G. 1998. On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In Proc. of AAAI-98, 326--333.

No context found.

B. Y. Choueiry and G. Noubir. On the computation of local interchangeability in discrete constraint satisfaction problems. In Proc. of AAAI'98, pages 326--333, 1998.

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Choueiry, B.Y., Noubir, G.: On the computation of local interchangeability in discrete constraint satisfaction problems. In: Proc. of AAAI-98. (1998) 326--333

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B. Choueiry and G. Noubir. On the computation of local interchangeability in discrete constraint satisfaction problems. In Proc. of AAAI'98, pages 326--333, Madison, WI, 1998.

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