Multicut Algorithms via Tree Decompositions

Pichler, Reinhard; Rümmele, Stefan; Woltran, Stefan

doi:10.1007/978-3-642-13073-1_16

Cited by 6 publications

(3 citation statements)

References 20 publications

(24 reference statements)

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“…Finding the optimal solution is NP-hard also for the planar case; however, the planar separator theorem (Lipton and Tarjan 1979) states that a bisection, in which the biggest set contains at most two thirds of the vertices and whose separator contains O( √ n) vertices can be found in linear time. Other related problems are the multicut problems (Pichler et al 2010), in which the aim is to find the minimal set of edges (or nodes) such that given pairs of nodes are no longer connected. In our case, instead, the aim is to disconnect a possibly small part of the network while keeping connected all the rest.…”

Section: Resultsmentioning

confidence: 99%

Optimal placement of valves in a water distribution network with CLP(FD)

Cattafi

Gavanelli

Nonato

et al. 2011

Theory and Practice of Logic Programming

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This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to solve a hard combinatorial problem. This application deals with one aspect of the design of a water distribution network, i.e., the valve isolation system design.We take the formulation of the problem by Giustolisi and Savić (2008) and show how, thanks to constraint propagation, we can get better solutions than the best solution known in the literature for the Apulian distribution network.We believe that the area of the so-called hydroinformatics can benefit from the techniques developed in Constraint Logic Programming and possibly from other areas of logic programming, such as Answer Set Programming.

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Section: Resultsmentioning

confidence: 99%

Optimal placement of valves in a water distribution network with CLP(FD)

Cattafi

Gavanelli

Nonato

et al. 2011

Theory and Practice of Logic Programming

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show abstract

“…Other related problems are the multicut problems [23], in which the aim is to find the minimal set of edges (or nodes) such that given pairs of nodes are no longer connected. In our case, instead, the aim is to disconnect a possibly small part of the network while keeping connected all the rest.…”

Section: Related Workmentioning

confidence: 99%

An ASP approach for the valves positioning optimization in a water distribution system

Gavanelli

Nonato

Peano

2013

Journal of Logic and Computation

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Abstract. Positioning of valves is a real-life issue in Water DistributionSystem design and, currently, it is usually addressed by hand by hydraulic engineers, or by means of genetic algorithms, that give no assurance of optimality. Since a given valves placement identifies a sectorization of the WDS in several isolable portions, the valves positioning problem can be seen as a variant of the well known graph partitioning, which is a hard combinatorial problem. [2] showed recently that Computational Logic can provide technologies and techniques that can be exploited to model and achieve the optimal partition of the water network (i.e., the optimal positioning of valves). In particular, they tackled the optimization of the valves positioning through a two player game model, giving a Constraint Logic Programming formalization to solve it effectively. The aim of this paper, instead, is to investigate the potential of Answer Set Programming in this practical application; evaluation is in terms both of language expressivity and solving efficiency. Results are discussed for different ASP models and a comparison with the CLP(FD) technique shown by [2] will be given.

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“…An FPT 2-approximation algorithm was given in [36] for Edge Multicut: in time O * (2 O(p log p) ), one can find a solution of size 2p if a solution of size p exists. There is no obvious FPT algorithm for the problem even on bounded-treewidth graphs, although one can obtain linear-time algorithms if the treewidth remains bounded after adding an edge s i t i for each terminal pair [23,40]. A PTAS is known for bounded-degree graphs of bounded treewidth [6].…”

Section: Introductionmentioning

confidence: 99%

Fixed-parameter tractability of multicut parameterized by the size of the cutset

Marx

Razgon

2011

Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing

102

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Given an undirected graph G, a collection {(s 1 , t 1 ), . . . , (s k , t k )} of pairs of vertices, and an integer p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal of S disconnects every s i from the corresponding t i . Vertex Multicut is the analogous problem where S is a set of at most p vertices. Our main result is that both problems can be solved in time 2 O(p 3 ) · n O(1) , i.e., fixed-parameter tractable parameterized by the size p of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f (p) · n O(1) exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset. * A preliminary version of the paper was presented at STOC 2011 [37].

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Multicut Algorithms via Tree Decompositions

Cited by 6 publications

References 20 publications

Optimal placement of valves in a water distribution network with CLP(FD)

Optimal placement of valves in a water distribution network with CLP(FD)

An ASP approach for the valves positioning optimization in a water distribution system

Fixed-parameter tractability of multicut parameterized by the size of the cutset

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