Results 1  10
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12
Treewidth: Computational experiments
, 2001
"... Many NPcomplete graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to nd (almo ..."
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Cited by 45 (9 self)
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Many NPcomplete graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to nd (almost) optimal solutions or lower bounds for diverse optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Although for xed k, linear time algorithms exist to solve the decision problem \treewidth k", their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on wellknown algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identied by these methods. For other graphs, however, more sophisticated techniques are necessary.
Rapid protein sidechain packing via tree decomposition
 Research in Computational Molecular Biology, Lecture Notes in Computer Science
, 2005
"... Abstract. This paper proposes a novel tree decomposition based sidechain assignment algorithm, which can obtain the globally optimal solution of the sidechain packing problem very efficiently. Theoretically, the computational complexity of this algorithm is O((N +M)n tw+1 rot) where N is the numbe ..."
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Cited by 26 (1 self)
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Abstract. This paper proposes a novel tree decomposition based sidechain assignment algorithm, which can obtain the globally optimal solution of the sidechain packing problem very efficiently. Theoretically, the computational complexity of this algorithm is O((N +M)n tw+1 rot) where N is the number of residues in the protein, M the number of interacting residue pairs, nrot the average number of rotamers for each residue and tw( = O(N 2 3 log N)) the tree width of the residue interaction graph. Based on this algorithm, we have developed a sidechain prediction program SCATD (Side Chain Assignment via Tree Decomposition). Experimental results show that after the Goldstein DEE is conducted, nrot is around 3.5, tw is only 3 or 4 for most of the test proteins in the SCWRL benchmark and less than 10 for all the test proteins. SCATD runs up to 90 times faster than SCWRL 3.0 on some large proteins in the SCWRL benchmark and achieves an average of five times faster speed on all the test proteins. If only the postDEE stage is taken into consideration, then our treedecomposition based energy minimization algorithm is more than 200 times faster than that in SCWRL 3.0 on some large proteins. SCATD is freely available for academic research upon request. 1
Soft arc consistency revisited
 Artificial Intelligence
"... The Valued Constraint Satisfaction Problem (VCSP) is a generic optimization problem defined by a network of local cost functions defined over discrete variables. It has applications in Artificial Intelligence, Operations Research, Bioinformatics and has been used to tackle optimization problems in o ..."
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Cited by 21 (3 self)
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The Valued Constraint Satisfaction Problem (VCSP) is a generic optimization problem defined by a network of local cost functions defined over discrete variables. It has applications in Artificial Intelligence, Operations Research, Bioinformatics and has been used to tackle optimization problems in other graphical models (including discrete Markov Random Fields and Bayesian Networks). The incremental lower bounds produced by local consistency filtering are used for pruning inside Branch and Bound search. In this paper, we extend the notion of arc consistency by allowing fractional weights and by allowing several arc consistency operations to be applied simultaneously. Over the rationals and allowing simultaneous operations, we show that an optimal arc consistency closure can theoretically be determined in polynomial time by reduction to linear programming. This defines Optimal Soft Arc Consistency (OSAC). To reach a more practical algorithm, we show that the existence of a sequence of arc consistency operations which increases the lower bound can be detected by establishing arc consistency in a classical Constraint Satisfaction Problem (CSP) derived from the original cost function network. This leads to a new soft arc consistency method, called,Virtual Arc Consistency which produces improved lower bounds compared with previous techniques and which can solve submodular cost functions. These algorithms have been implemented and evaluated on a variety of problems, including two difficult frequency assignment problems which are solved to optimality for the first time. Our implementation is available in the open source toulbar2 platform.
Tree decompositions of graphs: Saving memory in dynamic programming
 CTW 2004: CologneTwente Workshop on Graphs and Combinatorial Optimization, Villa Vigoni (CO
, 2004
"... We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a treelike set covering problem. We substantiate our findings by experimental results. Our strategy has n ..."
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Cited by 10 (2 self)
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We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a treelike set covering problem. We substantiate our findings by experimental results. Our strategy has negligible computational overhead concerning running time but achieves memory savings for nice tree decompositions and path decompositions between 60 % and 98%.
Algorithms for the Radio Link Frequency Assignment Problem
, 1999
"... The radio link frequency assignment problem occurs when a network of radio links has to be established. Each link must be assigned an operating frequency from a given domain. The assignment has to satisfy certain restrictions so as to limit the interference between links. The number of frequencie ..."
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Cited by 9 (1 self)
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The radio link frequency assignment problem occurs when a network of radio links has to be established. Each link must be assigned an operating frequency from a given domain. The assignment has to satisfy certain restrictions so as to limit the interference between links. The number of frequencies used is to be minimized. Problems of this type were investigated by a consortium consisting of research groups from Delft, Eindhoven, London, Maastricht, Norwich, and Toulouse. The participants developed optimization algorithms based on branchandcut and constraint satisfaction, and approximation techniques including a variety of local search methods, genetic algorithms, neural networks, and potential reduction. These algorithms were tested and compared on a set of reallife instances.
Idwalk : A candidate list strategy with a simple diversification device
 CP 2004: Lecture Notes in Computer Science
, 2004
"... Abstract. This paper presents a new optimization metaheuristic called ID Walk (Intensification/Diversification Walk) that offers advantages for combining simplicity with effectiveness. In addition to the number S of moves, ID Walk uses only one parameter Max which is the maximum number of candidate ..."
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Cited by 9 (4 self)
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Abstract. This paper presents a new optimization metaheuristic called ID Walk (Intensification/Diversification Walk) that offers advantages for combining simplicity with effectiveness. In addition to the number S of moves, ID Walk uses only one parameter Max which is the maximum number of candidate neighbors studied in every move. This candidate list strategy manages the Max candidates so as to obtain a good tradeoff between intensification and diversification. A procedure has also been designed to tune the parameters automatically. We made experiments on several hard combinatorial optimization problems, and ID Walk compares favorably with correspondingly simple instances of leading metaheuristics, notably tabu search, simulated annealing and Metropolis. Thus, among algorithmic variants that are designed to be easy to program and implement, ID Walk has the potential to become an interesting alternative to such recognized approaches. Our automatic tuning tool has also allowed us to compare several variants of ID Walk and tabu search to analyze which devices (parameters) have the greatest impact on the computation time. A surprising result shows that the specific diversification mechanism embedded in ID Walk is very significant, which motivates examination of additional instances in this new class of “dynamic ” candidate list strategies. 1
New Upper Bound Heuristics for Treewidth
, 2004
"... In this paper, we introduce and evaluate some heuristics to find an upper bound on the treewidth of a given graph. Each of the heuristics selects the vertices of the graph one by one, building an elimination list. The heuristics differ in the criteria used for selecting vertices. These criteria depe ..."
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Cited by 9 (4 self)
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In this paper, we introduce and evaluate some heuristics to find an upper bound on the treewidth of a given graph. Each of the heuristics selects the vertices of the graph one by one, building an elimination list. The heuristics differ in the criteria used for selecting vertices. These criteria depend on the fillin of a vertex and the related new notion of the fillinexcludingoneneighbor. In several cases, the new heuristics improve the bounds obtained by existing heuristics.
A note on CSP graph parameters
, 1999
"... Several graph parameters such as induced width, minimum maximum clique size of a chordal completion, ktree number, bandwidth, front length or minimum pseudotree height are available in the CSP community to bound the complexity of specific CSP instances using dedicated algorithms. After an intro ..."
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Cited by 8 (0 self)
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Several graph parameters such as induced width, minimum maximum clique size of a chordal completion, ktree number, bandwidth, front length or minimum pseudotree height are available in the CSP community to bound the complexity of specific CSP instances using dedicated algorithms. After an introduction to the main algorithms that can exploit these parameters, we try to exhaustively review existing parameters and the relations that may exist between then. In the process we exhibit some missing relations. Several existing results, both old results and recent results from graph theory and Cholesky matrix factorization technology [BGHK95] allow us to give a very dense map of relations between these parameters. These results strongly relate several existing algorithms and answer some questions which were considered as open in the CSP community. Warning: this document is a working paper. Some sections may be incomplete or currently being worked out ([GJC94] degree of cyclicity not ...
Lower bounds for Minimum Interference Frequency Assignment Problems
, 1999
"... In this paper we describe a new lower bound procedure for the minimum interference frequency assignment problem (MIFAP). In the MIFAP we have to assign frequencies to transmitterreceiver pairs in suchaway that the cumulativeinterference in the communication network is minimized. Mainly due to the ..."
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Cited by 7 (2 self)
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In this paper we describe a new lower bound procedure for the minimum interference frequency assignment problem (MIFAP). In the MIFAP we have to assign frequencies to transmitterreceiver pairs in suchaway that the cumulativeinterference in the communication network is minimized. Mainly due to the fairly large number of available frequencies, exact methods fail to solve the more difficult instances. In this paper we describe a procedure that produces a nondecreasing sequence of lower bounds. In each iteration of the algorithm we have to solve MIFAPs that are substantially smaller than the original instance. These subproblems can be solved with either integer programming techniques or a dynamic programming algorithm based on a tree decomposition of the underlying graph. Computational results show that integer programming and dynamic programming supply very good results.