B.W. Benson and E. Freuder. Interchangeability preprocessing can improve forward checking search. In Proc. of the 10th ECAI, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in [13] This study measured the occurrence of NI sets depending on the configuration of the CSP and found that: Only problems with low density allow NI values; the number of NI values become near to 0 for a density higher then 0. 4 (this also corresponds to Benson and Freuder s results in [14]) For problems with low density the number of NI values increases with the number of resources. In general, the number of NI values decreases with the size of the problem. These results indicate that NI interchangability is quite restricted in its domain of applicability and is one of ....

B.W. Benson and E. Freuder. Interchangeability Preprocessing can Improve Forward Checking Search. In Proc. of the 10 th Ecai, pages 28-30, Vienna, Austria, 1992.

....showed that neighbourhood interchangeability always implies full interchangeability and can therefore be used as an approximation. He also provided an e#cient algorithm for computing neighborhood interchangeability [20] and investigated its use for preprocessing CSP before searching for solutions [22]. 3 Interchangeability in Soft CSPs In soft CSPs, there are not any crisp notion of consistency. In fact, each tuple is a possible solution, but with di#erent level of preference. Therefore, in this framework, the notion of interchangeability become finer: to say that values a and b are ....

Benson, B., Freuder, E.: Interchangeability Preprocessing can Improve Forward Checking Search. In Proc. of the 10 th Ecai, pages 28-30, Vienna, Austria (1992)

....showed that neighbourhood interchangeability always implies full interchangeability and can therefore be used as an approximation. He also provided an e#cient algorithm for computing neighborhood interchangeability [14] and investigated its use for preprocessing CSP before searching for solutions [16]. 3 Interchangeability in Soft CSPs In soft CSPs, there are not any crisp notion of consistency. In fact, each tuple is a possible solution, but with di#erent level of preference. Therefore, in this framework, the notion of interchangeability become finer: to say that values a and b are ....

Benson, B., Freuder, E.: Interchangeability Preprocessing can Improve Forward Checking Search. In Proc. of the 10 th Ecai, pages 28-30, Vienna, Austria (1992)

....interchangeability capture the equivalence among values of a variable in a discrete constraint satisfaction problem. 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 ....

....full interchangeable sets might be a quite costly operation as it may require computing all the solutions. A localised but stronger condition than full interchangeability was further proposed: neighborhood interchangeability (NI) This can be computed in polynomial time. Benson and Freuder [3] studied then for which CSP structures NI sets are likely to occur. They notice that only problems of small density ( 0.4) one can find NI sets. For problems with small density, the number of NI sets increases with the domain size. Other experiments confirmed these results , see Choueiry and ....

B.W. Benson and E. Freuder. Interchangeability Preprocessing can Improve Forward Checking Search. In Proc. of the 10 th Ecai, pages 28-30, Vienna, Austria, 1992.

....are biased to one particular problem leaving one to doubt whether or not they apply to other CSP domains. To overcome this bias, many papers have attempted to classify the performance of CSP algorithms on randomly generated binary CSPs [ Gaschnig, 1979; Haralick and Elliot, 1980; Dechter, 1990; Benson and Freuder, 1992; Dechter and Meiri, 1994; van Run, 1994 ] In a binary CSP all constraints have arity 2. A binary CSP can be interpreted as a graph in which the nodes represent the variables, the edges represent the constraints, and the contents of the nodes are the domains. Random binary CSPs are parameterized ....

B. Benson and E. Freuder. Interchangeability preprocessing can improve forward checking search. In Proceedings ECAI-92, 1992.

....3 Formulation of a GCSP A CSP is defined by a set of variables belonging to a finite domain of values and a set of constraints on these variables [Mac77] To solve a CSP means to instantiate the variables in order to satisfy all the constraints. Many research works are related to CSP [DD87, BF92, Mac77, DSa88a, Ber92] We call GCSP (Geometric Constraint Satisfaction Problem) a CSP with geometric constraints on objects to place and to size. An object is characterized by its location, its orientation, its shape and its sizes. The position of an object is the position of a particular point ....

B. Benson and E. Freuder. Interchangeability preprocessing can improve forward checking search. In Proc. ECAI 92, pages 28--30, 1992.

....In [3] Freuder introduces the notion of interchangeability to cluster values of a variable that belong to the same solutions. Removing some interchangeable values before generating all the solutions using Forward Checking has been proved successful on loose and sparse connected problems (see [1]) In [6] Backtracking and Forward Checking are extended to operate on a cross product representation of partial consistent assignments. The corresponding algorithms BT CPR and FC CPR generate a partition of the set of solutions whose elements are cross products of sub domains of the variables. ....

Benson, B. W. and Freuder, E.C.: Interchangeability preprocessing can improve Forward-Checking search, Proc. of ECAI-92, pp. 28-30, 1992.

....constraints for a general CSP. The third approach exploits such problem specific characteristics as structure of the constraint graph [14, 21] and properties of the constraints and domains [53, 43, 36] Other problem characteristics include decomposability [51] symmetries and interchangeability [4, 22, 20]. This class of techniques is also problem and domain specific. The fourth approach enhances basic backtracking search with such techniques as backmarking [23, 24, 30] and backjumping [25, 26, 49] The fifth approach is to entirely replace propagation based techniques, which are algorithmic in ....

B.W. Benson Jr. and E.C. Freuder. Interchangeability preprocessing can improve forward checking search. In Proceedings of the 10th European Conference on Artificial Intelligence, pages 28--30, 1992.

....Now we want to invistigate the indicated performance improvement of our augmented search technique by experimental analysis. We will test both interchangeability and symmetry and compare them on two kind of problems: I) randomlly generated CSP s, we use the same test model as proposed in Freuder ([8]) II) the pigeon hole problem which is known to be hard, is solved using symmetries with a linear complexity, however interchangeability get no use for this problem. 5.1 The experiment model Random CSP s are characterized by the following four parameters: 1) n, the number of variables. 2) a, ....

....of variables It can be seen in figure 6 that the effect of both symmetry and interchangeability grows if the problem increase. The variable size steps from 6 to 10, a is fixed on 5, t and d are from the interval [0.1 0. 4] the profitable ranges for the use of interchangeability as claimed in [8]) It can also be seen that FC 0 SV definitily beats FC 0NI at these problems type. 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 2 4 6 8 10 12 14 16 FC FC NI 3 3 3 3 3 3 3 FC SV Fig.7. FC and FC NI effects on Pigeon hole problem. Figure 8 shows that the complexity of FC0 SV for ....

E. Freuder and W. Benson. Interchangeability preprocessing can improve forward checking search. In proc. ECAI, 1992.

....the various kinds of interchangeability discovered during decomposition by the VAD heuristic. Figure 5: A simple resource allocation problem. The problem domain is the allocation of operating rooms and technicians to hospital operations. The example shown in Fig. 5 has the following CSP parameters [4, 33]: hn; a; t; di = 22; 8; 0:091; 0:376. In Fig. 6 , we show the tree structure generated by application of the VAD Figure 6: A simple resource allocation problem after decomposition by the VAD heuristic. heuristic and the resources delayed at the branching nodes. For each leaf cluster, we display ....

....an open question: the sets discovered by the VAD may be only subsets of the largest possible ones, and some possible sets may simply be missed. We have tested our algorithm on data from a hospital case study. In terms of CSP measures, the tests show the following order parameters, hn; a; t; di see [4, 33]: ffl number of variables n = 22 : 72, ffl maximum domain size a = 5 : 31, ffl constraint tightness t = jforbidden tuplesj jall tuplesj = 0:037 : 0:108, and ffl constraint density d = e Gammae min emax Gammae min = 0:376 : 0:570, where e is the number of constraints, e ....

Brent W. Benson and Eugene C. Freuder. Interchangeability Preprocessing Can Improve Forward Checking Search. In Proc. of the 10 th ECAI, pages 28--30, Vienna, Austria, 1992.

....they do not get al..ong well with the surgeon, the human operator rejected this decision. Interestingly enough, for those cases where no solutions existed, the backtrack search would thrash forever and 7 In terms of CSP measures, the tests show the following order parameters, n; a; t; d see [2, 25]: number of variables n = 22 to 72, mean domain size a = 5 to 31, constraint tightness t = P forbidden tuples P all tuples = 0.037 to 0.108, constraint density d = e Gammae min emax Gammae min = 0.376 to 0.570, where e is the number of constraints, e min = n Gamma 1) and e max = ....

Brent W. Benson and Eugene C. Freuder. Interchangeability Preprocessing Can Improve Forward Checking Search. In Proc. of the 10 th ECAI, pages 28--30, Vienna, Austria, 1992.

....are presented and formalized in [32, 18] Fig. 7 illustrates two main properties: 1) The downward solution property guarantees that a solution found in the abstract space can be mapped back to a feasible solution 4 In terms of CSP measures, the tests show the following order parameters [3, 24]: hn; a; t; di = h22 : 72, 5 : 31, 0:037 : 0:108, 0:376 : 0:570i. n is the number of variables, a the maximumdomain size, t = jforbidden tuplesj jall tuplesj the constraint tightness, d = e Gammae min emax Gammae min the constraint density, e the number of constraints, e ....

Brent W. Benson and Eugene C. Freuder. Interchangeability Preprocessing Can Improve Forward Checking Search. In Proc. of the 10 th ECAI, pages 28--30, Vienna, Austria, 1992.

....(i; b) Definition 10 [FRE 91] Soient (i; a) et (i; b) deux valeurs du meme domaine D i d un CSP Pi. i; b) est voisinage substituable a (i; a) si et seulement si N(i; a) N(i; b) Remarquons que cette notion est une affaiblissement de la notion d interchangea bilite etudiee par [FRE 91] BEN 92] et [HAS 93] deux valeurs (i; a) et (i; b) sont voisinage interchangeables si et seulement si (i; a) est voisinage substituable a (i; b) et (i; b) est voisinage substituable a (i; a) i.e. N(i; a) N(i; b) De meme, deux valeurs sont interchangeables si chacune d elles est substituable a ....

....nous avons fait varier q dans les intervalles [0:1; 0:15] 0:15; 0:20] 0:75; 0:80] par pas de 0:01, et calcule la moyenne des resultats pour chacun des intervalles. Nos methodes ont ete efficaces avec les petites valeurs de p et de q (ceci recoupe les resultats presentes dans [BEN 92] seules les courbes concernant l intervalle q 2 [0:20; 0:25] sont presentees par la suite, mais elles recoupent les resultats obtenus pour des valeurs de q inferieures a 0:35. Notre etude s est decomposee en plusieurs etapes : Nous avons compare FC et VS FC sur un petit nombre de problemes. ....

BENSON JR B. et FREUDER E., Interchangeability preprocessing can improve forward checking search. In : Proceedings of ECAI'92, p. 28--30, Vienne, Autriche, Aout 1992.

....(i; b) Definition 10 [FRE 91] Soient (i; a) et (i; b) deux valeurs du meme domaine D i d un CSP Pi. i; b) est voisinage substituable a (i; a) si et seulement si N(i; a) N(i; b) Remarquons que cette notion est une affaiblissement de la notion d interchangea bilite etudiee par [FRE 91] BEN 92] et [HAS 93] deux valeurs (i; a) et (i; b) sont voisinage interchangeables si et seulement si (i; a) est voisinage substituable a (i; b) et (i; b) est voisinage substituable a (i; a) i.e. N(i; a) N(i; b) De meme, deux valeurs sont interchangeables si chacune d elles est substituable a ....

....dans la partie 3.1. L exploitation de cette propriete est au centre des techniques algorithmiques presentees dans la suite de cet article. Travaux connexes interchangeabilite. Ces travaux concernent essentiellement l utilisation de la voisinage interchangeabilite . Benson et Freuder [BEN 92] montrent de facon experimentale que le pre filtrage des problemes par elimination des valeurs interchangeables peut se re veler profitable pour certains types de problemes. Haselbock ( HAS 93] utilise des versions affaiblies de l interchangeabilite pour ameliorer d une part les algorithmes de ....

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BENSON JR B. et FREUDER E., Interchangeability preprocessing can improve forward checking search. In : Proceedings of ECAI'92, p. 28--30, Vienne, Autriche, Aout 1992.

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B.W. Benson and E. Freuder. Interchangeability preprocessing can improve forward checking search. In Proc. of the 10th ECAI, 1992.

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B.W. Benson and E.C. Freuder. Interchangeability Preprocessing Can Improve Forward Checking Search. In Proc. of the 10 th ECAI, pages 28-30, 1992.

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Benson, B., Freuder, E.: Interchangeability preprocessing can improve forward checking search. In: Proc. of the 10th ECAI, Vienna, Austria. (1992) 28--30

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B.W. Benson and E. Freuder. Interchangeability preprocessing can improve forward checking search. In Proc. of the 10th ECAI, 1992.

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Brent W. Benson and Eugene C. Freuder. Interchange- ability Preprocessing Can Improve Forward Checking Search. In Proc. of the 10 h ECAI, pages 28-30, Vi- enna, Austria, 1992.

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Brent W. Benson and Eugene C. Freuder. Interchangeability Preprocessing Can Improve Forward Checking Search. In Proc. of the 10 th ECAI, pages 28--30, Vienna, Austria, 1992.

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