Using ILP/SAT to Determine Pathwidth, Visibility Representations, and other Grid-Based Graph Drawings

Biedl, Thérèse; Bläsius, Thomas; Niedermann, Benjamin; Nöllenburg, Martin; Prutkin, Roman; Rutter, Ignaz

doi:10.1007/978-3-319-03841-4_40

Cited by 13 publications

(28 citation statements)

References 31 publications

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“…Solano and Pioro proposed in [37] an exact branch and bound algorithm to compute the pathwidth of graphs, that checks all possible layout of the nodes and keep the best one. A mixed integer linear programming formulation (MILP) has been proposed in [2,37] and a dynamic programming algorithm (exponential both in time and space) is described in [6]. None of these methods handle graphs with more than 30 nodes.…”

Section: Practical Computation Of Pathwidthmentioning

confidence: 99%

“…None of these methods handle graphs with more than 30 nodes. As far as we know, the best practical exact algorithm for computing the pathwidth of graphs with more than 30 nodes is based on a SAT formulation of the problem that is solved using Constraint Programming solver [2]. Heuristics.…”

Section: Practical Computation Of Pathwidthmentioning

confidence: 99%

“…When the time is up, we return the best solution found so far and record it as an upper-bound on the vertex-separation of the input digraph. Following [2], we set this limit to 10 min.…”

Section: Bab-gppmentioning

confidence: 99%

“…In [2], an algorithm to compute the pathwidth of graphs is designed by formulating the PATHWIDTH problem as a Boolean satisfiability testing (SAT) instance and solving this SAT instance using the M iniSat solver [26]. No implementations are provided but the algorithm has been tested on the Rome graphs dataset [34].…”

Section: Milp Some Mixed Integer Linear Programming Formulations Formentioning

confidence: 99%

“…Table 2: Repartition of (un)solved instances for the Rome graph Instance. In [2], the performance of the SAT algorithm has been evaluated using this benchmark. With 10 min.…”

Section: Comparison Of Bab-gpp With Sat On the Rome Graphs Datasetmentioning

confidence: 99%

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Experimental Evaluation of a Branch and Bound Algorithm for Computing Pathwidth

Coudert

Mazauric

Nisse

2014

Experimental Algorithms

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It is well known that many NP-hard problems are tractable in the class of bounded pathwidth graphs. In particular, path-decompositions of graphs are an important ingredient of dynamic programming algorithms for solving such problems. Therefore, computing the pathwidth and associated path-decomposition of graphs has both a theoretical and practical interest. In this paper, we design a Branch and Bound algorithm that computes the exact pathwidth of graphs and a corresponding path-decomposition. Our main contribution consists of several non-trivial techniques to reduce the size of the input graph (pre-processing) and to cut the exploration space during the search phase of the algorithm. We evaluate experimentally our algorithm by comparing it to existing algorithms of the literature. It appears from the simulations that our algorithm offers a significative gain with respect to previous work. In particular, it is able to compute the exact pathwidth of any graph with less than 60 nodes in a reasonable running-time (≤ 10 min.). Moreover, our algorithm also achieves good performance when used as a heuristic (i.e., when returning best result found within bounded time-limit). Our algorithm is not restricted to undirected graphs since it actually computes the vertex-separation of digraphs (which coincides with the pathwidth in case of undirected graphs). Nous évaluons expérimentalement notre algorithme en le comparant aux algorithmes proposés dans la littérature. Les simulations montrent que notre algorithme apporte un gain significatif par rapport aux algorithmes existants. Il est capable de calculer la valeur exacte de la pathwidth de tout graphe composé d'au plus 60 sommets en un temps raisonnable (moins de 10 minutes). De plus, notre algorithme montre de bonnes performances lorsqu'il est utilisé en heuristique (c'est-à-dire lorsqu'il retourne le meilleur résultat trouvé en un temps donné).Notre algorithme n'est pas spécifique au graphes non orientés car il permet de calculer la vertex-separation des digraphes (qui coïncide avec la pathwidth dans le cas des graphes non orientés).

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Section: Practical Computation Of Pathwidthmentioning

confidence: 99%

Section: Practical Computation Of Pathwidthmentioning

confidence: 99%

“…When the time is up, we return the best solution found so far and record it as an upper-bound on the vertex-separation of the input digraph. Following [2], we set this limit to 10 min.…”

Section: Bab-gppmentioning

confidence: 99%

Section: Milp Some Mixed Integer Linear Programming Formulations Formentioning

confidence: 99%

“…Table 2: Repartition of (un)solved instances for the Rome graph Instance. In [2], the performance of the SAT algorithm has been evaluated using this benchmark. With 10 min.…”

Section: Comparison Of Bab-gpp With Sat On the Rome Graphs Datasetmentioning

confidence: 99%

See 3 more Smart Citations

Experimental Evaluation of a Branch and Bound Algorithm for Computing Pathwidth

Coudert

Mazauric

Nisse

2014

Experimental Algorithms

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Using ILP/SAT to Determine Pathwidth, Visibility Representations, and other Grid-Based Graph Drawings

et al. 2013

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Abstract. We present a simple and versatile formulation of grid-based graph representation problems as an integer linear program (ILP) and a corresponding SAT instance. In a grid-based representation vertices and edges correspond to axisparallel boxes on an underlying integer grid; boxes can be further constrained in their shapes and interactions by additional problem-specific constraints. We describe a general d-dimensional model for grid representation problems. This model can be used to solve a variety of NP-hard graph problems, including pathwidth, bandwidth, optimum st-orientation, area-minimal (bar-k) visibility representation, boxicity-k graphs and others. We implemented SAT-models for all of the above problems and evaluated them on the Rome graphs collection. The experiments show that our model successfully solves NP-hard problems within few minutes on small to medium-size Rome graphs.

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