J.C. R egin. A filtering algorithm for constraints of difference in CSPs. In Proc. AAAI'94, pp 362-- 367. 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a high level of propagation with limited computation, specialized propagators, which take advantage of the constraint s structure, can be devised for particular classes of constraints. Examples of constraints for which specialized propagators have been devised are the all different constraint [15] and the cardinality constraint [16] We now describe the specialized propagators that were devised for the loosening approach. Distribution Propagator Since the distribution exception constraint is a generalization of the even distribution constraint, the same propagator is used on both. The ....

.... if runlen attvalue = RunLenAttribute(l) then intrunlength intrunlength LotSize(l) else BREAK end if end for if (intrunlength runlength) maxrunlength then remove b from Domain(s i ) end if end for end if runlength 0 end if end for 40 arc consistency propagator described in [15]. Such a propagator would remove more domain values but would also be more computationally expensive. 4.3 Branch and Bound Approach In this section we describe backtracking on a CSOP model with a branch and bound approach. For this approach, we begin with a loose bound on the evaluation function ....

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J-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proceedings of the Twelfth National Conference on Artificial Intelligence, pages 362--367, Seattle, Washington, 1994.

....number of marks. The table shows the number of branches explored during the search (the number of fails) and the CPU time (on a Silicon Graphics O2) both in finding the optimal solution (F) and in proving optimality thereafter (P) With the all different constraint, R egin s filtering algorithm [4] was used for efficiency. In all three representations, the search variables are those representing the marks, i.e. x i , i = 1; m, and are ordered lexicographically. Although the theory of the last section is concerned with generalized arc consistency applied to both the quaternary and ....

J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proceedings AAAI'94, volume 1, pages 362--367, 1994.

....with the all different constraint. The domains of x 1 ; x 2 are therefore reduced to D 1 = D 2 = f2; 3; 4; 5g. There are several different domain reduction algorithms that removes domain elements that are inconsistent with all different, varying in degree of efficiency and completeness [18, 20]. A feasible solution is found at node 4 that permits one to set z = 25. At node 5 another type of domain reduction, based on maintaining bounds consistency, can be applied [18] It infers from (2) that x 3 1 5 (z Gamma 4 minD 1 Gamma 3 minD 2 ) 6) where minD j is the smallest element in D j ....

J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proc. of the Twelfth National Conference on Artificial Intelligence (AAAI-94), pages 362--367, 1994.

....array of problems. Rather than restricting oneself to a narrow vocabulary that suits the solver, one identifies subsets of constraints that reflect a common modeling situation. These might be a permutation constraint, resource constrained scheduling constraints, bin packing constraints, etc. e.g. [19, 21, 4, 8, 7]) The specially structured group of constraints is represented by a single global constraint in the program, such as all different or cumulative. It invokes special purpose domain reduction algorithms that are based on prior analysis of constraints exhibiting this pattern. The two communities ....

J-C R'egin. A filtering algorithm for constraints of difference in CSPs. Technical Report R.R.LIRMM 93-068, LIRM, Dec 1993.

....primarily to the recent commercial success of constraint programming and its richer modeling resources. Constraint programming systems permit not only such logical constructions as disjunctions and implications [20, 21, 15] but they include high level symbolic constraints such as all different [18, 20] and scheduling constraints [1, 6] and other highly useful predicates that are foreign to a mathematical programming environment [1, 2, 7, 21] Variables need not even have numerical values, and they can appear in subscripts. The power of this modeling framework is dramatically illustrated by ....

J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proc. of the Twelfth National Conference on Artificial Intelligence (AAAI-94), pages 362--367, 1994.

....constraints over the members of the clique. For each CSP, we examine the constraint graph and extract such cliques, replacing the binary constraints they subsume by single alldifferent constraints denoting pairwise disequations between all variables involved. We use R egin s complete algorithm [12] for maintaining consistency. This transformation has the advantages of 1. reducing the number of constraints engaged in propagation, and 2. increasing propagation power. The clique extraction is done using a greedy algorithm. The aim is not to find the largest clique, but rather to find a set of ....

J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proc. of the Twelfth National Conference on Artificial Intelligence (AAAI-94), pages 362--367, 1994.

....number of marks. The table shows the number of branches explored during the search (the number of fails) and the CPU time (on a Silicon Graphics O2) both in finding the optimal solution (F) and in proving optimality thereafter (P) With the all different constraint, R egin s filtering algorithm [4] was used for efficiency. In all three representations, the search variables are those representing the marks, i.e. x i , i = 1; m, and are ordered lexicographically. Although the theory of the last section is concerned with generalized arc consistency applied to both the quaternary and ....

J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proceedings AAAI'94, volume 1, pages 362--367, 1994.

....Group Department of Computer Science University of Strathclyde email: ks,tw cs.strath.ac. uk August 30, 1999 1 Introduction Many constraint satisfaction problems can be naturally and efficiently modelled using non binary constraints like the all different and global cardinality constraints [14, 15, 16]. Certain classes of these non binary constraints are network decomposable [13, 5] as they can be represented by binary constraints on the same set of variables. Throughout this paper, we will abbreviate this to decomposable. For example, an all different constraint is decomposable into a clique ....

J-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proceedings of the AAAI-94, pages 362--367.

....; 8 1 i deg v (3) 1 C v i deg v 8 v 2 V ; 8 1 i deg v (4) This model features 2(jE j jMj) variables and 2(jE j jMj) 2 5(jE j jMj) constraints. Note that the number of constraints can be brought down to 6(jE j jMj) jV j if constraints (2) are handled globally at each vertex [9]. This also provides more powerful propagation. The model already describes cycle covers for our graph but those cycles need neither be elementary nor of limited size. v u w i j u u v v i j Fig. 5. Merging two chains. 2 Handling Constrained Cycles In this section we describe how we ....

J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proc. of the Twelfth National Conference on Artificial Intelligence (AAAI-94), pages 362--367, 1994.

....No. of Overall Maximum Problem Templates Templates Pressings Deviation Deviation Catfood 3 [0,1,1,1,1,2,3] 260,000 2.59 7.27 cartons [2,0,0,2,2,1,2] 120,000 [0,0,0,0,0,9,0] 17,778 Herb 3 [0,0,1,1,1,1,1,1,1,1, cartons 1,1,1,1,1,1,1,1,1,1, 1,1,1,2,3,3,3,3,3,4] 70,000 2.91 8. 70 [5,5,0,0,0,0,0,0,0,1, 1,1,1,2,2,2,2,2,2,3, 1,3,3,0,0,0,0,0,6,0] 10,000 [10,10,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 22,0,0,0,0,0,0,0,0,0] 909 Magazine 4 [1,0,0,1,0,0,1,0,1,1, 145,000 2.49 10.00 inserts 1,1,1,0,1,1,1,0,1,1, 1,1,1,1,0,1,0,1,1,1, 0,1,1,1,0,1,1,1,2,1, 1,1,1,0,2,2,1,1,0,1] 1,1,4,2,1,1,1,2,1,0, 60,250 1,1,0,1,1,1,0,0,1,0, 1,0,1,1,1,0,0,0,0,0, ....

.... propagation methods used in constraint programming work on constraints involving only two variables, or on constraints in which all but two of the variables have been assigned values (although for some special types of constraint more powerful propagation methods have been developed, e.g. [6]) In this problem, we do not always specify an upper tolerance on production of each variation in the CP model, so that any amount of over production is allowed, consistent with the other constraints. The only upper limit is then the overall limit given by the optimization constraint on P ....

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J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proceedings AAAI-94, volume 1, pages 362--367, 1994.

.... constraints expressing sums and scalar products of a list of domain variables, all different(L) constraining the elements of the list L to take distinct values. We have implemented a weak version simulating pairwise inequalities as well as a strong version based on R egin s algorithm [19]. element(I ; L; Y ) constraining the I:th element of L to be equal to Y , uses a consistency algorithm based on AC 4. cumulative(S; D;R;L) modelling a set of tasks with start times S, durations D, and resource need R, sharing a resource with capacity L [1] The implementation is based ....

....elements of a list all be distinct, may be modeled by O(N 2 ) disequations. If the same constraint is expressed as a single, global constraint, we get much better (O(N) space complexity, much smaller scheduler overhead, and the opportunity to employ a specialized, complete filtering algorithm [19] instead of merely mimicking the pairwise disequations. The need for specialized algorithms is most obvious on hard combinatorial problems [1,3,18] while the space complexity aspects can dominate on large instances of otherwise easy problems. Consequently, solvers based solely on indexicals can ....

J.-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proc. of the Twelfth National Conference on Artificial Intelligence (AAAI-94), pages 362--367, 1994.

.... (GAC) iff for any variable in a constraint and value that it is assigned, there exist compatible values for all the other variables in the constraint [ Mohr and Masini, 1988 ] Regin gives an efficient algorithm for enforcing generalized arc consistency on a set of all different constraints [ R egin, 1994 ] We can also maintain a level of consistency at every node in a search tree. For example, the MAC algorithm for binary Csps maintains arc consistency at each node in the search tree [ Gaschnig, 1979 ] As a second example, on a non binary problem, we can maintain generalized arcconsistency ....

J-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In Proc. of the 12th National Conference on AI, pages 362--367. 1994.

....the arrays of variables freq is indexed by the elements of transmitters that are records. This functionality is of primary importance to exploit sparsity in large scale models and to simplify the statement of many combinatorial optimization problems. nbCells = 25; nbFreqs = 256; nbTrans = [8 6 6 1 4 4 8 8 8 8 4 9 8 4 4 10 8 9 8 4 5 4 8 1 1]; distance = 16 1 1 0 0 0 0 0 1 1 1 1 1 2 2 1 1 0 0 0 2 2 1 1 1] 1 16 2 0 0 0 0 0 2 2 1 1 1 2 2 1 1 0 0 0 0 0 0 0 0] 1 2 16 0 0 0 0 0 2 2 1 1 1 2 2 1 1 0 0 0 0 0 0 0 0] 0 0 0 16 2 2 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1] 0 0 0 2 16 2 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1] 0 0 0 2 2 16 0 0 ....

.... s in Slots) team[p,w,s] onDomain; specifies that all the teams scheduled to play on week w must be different. It uses an aggregate operator all to collect the appropriate team variables by iterating over the periods and the slots and an annotation onDomain to enforce arc consitency. See [8] for a description on how to enforce arc consistency on this global constraint. The constraint distribute(occur,values,all(w in EWeeks s in Slots) team[p,w,s] extendedPropagation specifies that a team plays exactly twice over the course of the extended season. Its first argument specifies the ....

J-C. R'egin. A filtering algorithm for constraints of difference in CSPs. In AAAI94, proceedings of the Twelth National Conference on Artificial Intelligence, pages 362--367, Seattle, Washington, 1994.

....of allowed tuples of each binary constraint. For example, a constraint enforcing that the three variables x 1 , x 2 , and x 3 must all take different values can equivalently be replaced by the three binary constraints x 1 6= x 2 , x 1 6= x 3 , and x 2 6= x 3 . But, as it has been shown in [ R egin, 1994 ] non binary constraints lose a part of their semantics when encoded into a set of binary ones in this way. This leads, for example, to less pruning for arc consistency algorithms handling them. Hence, if we no longer want to consider the CSP as an academic problem we must be able to deal with ....

J.C. R'egin. A filtering algorithm for constraints of difference in CSPs. In AAAI'94, pages 362--367, Seattle WA.

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J.C. R egin. A filtering algorithm for constraints of difference in CSPs. In Proc. AAAI'94, pp 362-- 367. 1994.

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J-C. R egin. A filtering algorithm for constraints of difference in CSPs. In Proc. AAAI'94, pages 362--367. AAAI, 1994.

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R'egin, J.C. "A filtering algorithm for constraints of difference in CSPs" In AAAI-94, Proceedings of the Twelfth National Conference on Artificial Intelligence. 1994.

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R'egin, J. C. "A filtering algorithm for constraints of difference in CSPs" In AAAI94, Proceedings of the Twelfth National Conference on Artificial Intelligence. 1994.

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