R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In Proceedings of CP-99, LNCS 1520, pages 72--86, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....point which will prune parts of the search tree symmetrical to those already explored. Symmetry breaking therefore acts alongside the search strategy, co operating with it. We present a general method for symmetry breaking during search (SBDS) The approach was introduced by Backofen and Will [2], with an application to geometric constraints in protein structure prediction in an earlier paper [1] A less general method which also removes symmetries during search is described by Meseguer and Torras [7] We show in detail how SBDS can be implemented with minimal overhead in ILOG Solver, a ....

....expressing the effect of each symmetry on the branching constraint. For instance, if the branching decision were between var val and var val, in (1) 6= is replaced by . We describe how SBDS can be implemented with minimal overhead in cpu time and minimal effort from the programmer. We rely on [2] for proofs of correctness of the method. 3 IMPLEMENTATION OF SBDS To implement SBDS in ILOG Solver, we provide a new search function IlcGenerateSym to replace Solver s IlcGenerate. IlcGenerate searches by first choosing a variable var according to some userspecified strategy. Then it chooses a ....

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R. Backofen and S. Will, `Excluding Symmetries in Concurrent Constraint Programming', in Principles and Practice of Constraint Programming - CP'99, ed., J. Jaffar, LNCS 1713, pp. 73--87. Springer, (1999).

....remove symmetry before search starts [Pug93] A second method adds symmetry breaking constraints during search, as embodied by the SBDS system [GS00] Upon backtracking, SBDS adds symmetry breaking constraints that prune parts of the search tree symmetrical to those already explored. See also [BW99] for a related approach. Third, symmetry may also be broken through a heuristic variable ordering, directing the search towards subspaces with a high density of non symmetric states by breaking as many symmetries as possible with each new variable assignment. The variety maximisation heuristic ....

R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In J. Jaffar, editor, Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming, pages 73--87. Springer-Verlag, 1999. Lecture Notes in Computer Science 1713.

....Sym , where Sym ) is the group of permutations of the columns 2 ( Now, the following matrix is canonically labelled wrt row slices and the sequence of groups indicated next to each row: 1. 4] 5. 7] [1,2][3,4] 5,6] 7] 1] 2] 3] 4] 5] 6] 7] Canonically labelling the rows makes the columns lexicographically ordered, and vice versa: Theorem 3 If is a 2 d matrix with canonically labelled rows, then e . 0. 21 . 31 (1) for all 4 65 . In other words, the ....

.... , where Sym ) is the group of permutations of the columns 2 ( Now, the following matrix is canonically labelled wrt row slices and the sequence of groups indicated next to each row: 1. 4] 5. 7] 1,2] 3,4] 5,6] 7] [1][2] 3] 4] 5] 6] 7] Canonically labelling the rows makes the columns lexicographically ordered, and vice versa: Theorem 3 If is a 2 d matrix with canonically labelled rows, then e . 0. 21 . 31 (1) for all 4 65 . In other words, the columns of are in ....

[Article contains additional citation context not shown here]

R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In J. Jaffar, editor, CP'99, pages 73--87. Springer-Verlag, 1999. LNCS 1713.

.... [Sym S (k n 1 1 : n) where Sym S (i : j) is the group of permutations of the columns i; j. Now, the following matrix is canonically labelled wrt row slices and the sequence of groups indicated next to each row: 0 0000111 0011001 0101010 1 A [1. 4] 5. 7] [1,2][3,4] 5,6] 7] 1] 2] 3] 4] 5] 6] 7] Canonically labelling the rows makes the columns lexicographically ordered, and vice versa: Theorem 3 If x is a 2 d matrix with canonically labelled rows, then x i;1 : x i;n lex x i 1;1 : x i 1;n (1) for all 1 i m. In other words, the columns ....

....1 1 : n) where Sym S (i : j) is the group of permutations of the columns i; j. Now, the following matrix is canonically labelled wrt row slices and the sequence of groups indicated next to each row: 0 0000111 0011001 0101010 1 A [1. 4] 5. 7] 1,2] 3,4] 5,6] 7] [1][2] 3] 4] 5] 6] 7] Canonically labelling the rows makes the columns lexicographically ordered, and vice versa: Theorem 3 If x is a 2 d matrix with canonically labelled rows, then x i;1 : x i;n lex x i 1;1 : x i 1;n (1) for all 1 i m. In other words, the columns of x are in ....

[Article contains additional citation context not shown here]

R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In J. Jaffar, editor, CP'99, pages 73--87. Springer-Verlag, 1999. LNCS 1713.

....allow arbitrary forms of symmetry. None of the approaches discussed above meet al..l our aims. We present SBDS, a general method of breaking symmetry during search. It acts alongside the search strategy, co operating with it. SBDS is essentially similar to the method introduced by Backofen and Will [2] for concurrent constraint programming, with an application to the protein folding problem [1] We give simple correctness proofs for SBDS, and extend this earlier work in a number of ways. We show in detail how our approach can be implemented with minimal overhead in the constraint programming ....

R. Backofen and S. Will. Excluding Symmetries in Concurrent Constraint Programming. In Workshop on Modeling and Computing with Concurrent Constraint Programming, 1998.

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R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In Proceedings of CP-99, LNCS 1520, pages 72--86, 1999.

No context found.

R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In Proceedings of CP-99, LNCS 1520, pages 72--86, 1999.

No context found.

R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In Proceedings of CP-99, LNCS 1520, pages 72--86, 1999.

No context found.

R. Backofen and S. Will. Excluding symmetries in concurrent constraint programming. In Proceedings of CP-99, LNCS 1520, pages 72--86, 1999.

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