SAT-Based Approaches to Treewidth Computation: An Evaluation

Berg, Jeremias; Järvisalo, Matti

doi:10.1109/ictai.2014.57

Cited by 23 publications

(18 citation statements)

References 24 publications

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“…We implemented the SAT-encoding for treecut width and the two SAT-encodings for treedepth and evaluated them on various benchmark instances; for comparison we also computed the pathwidth and treewidth of all graphs using the currently best performing SAT-encodings [34,25]; note that [34] is still the best-known SAT-encoding for treewidth, since the performance gains of later algorithms [2,1] are almost entirely due to preprocessing, whereas the employed SATencoding is virtually identical. Our benchmark instances include 39 famous named graphs from the literature [35], various standard graphs such as complete graphs (K n ), complete bipartite graphs (K n,n ), paths (P n ), cycles (C n ), complete binary trees (B n ), and grids (G n,n ) as well as random graphs.…”

Section: Methodsmentioning

confidence: 99%

“…Using this simpler definition together with an explicit preprocessing procedure for general graphs (presented in Section 2.3), we introduce a SATencoding for 3-edge-connected graphs based on a partitionbased characterisation of treecut width in Section 3. As our experiments show, the encoding performs extraordinary well; outperforming even our arguably much simpler encoding for treedepth and the current best-performing SATencoding for treewidth [1,2,34].…”

Section: Treecut Widthmentioning

confidence: 96%

“…We have already mentioned the successful application of SAT-encodings for graph decompositions above [1,2,18,25,34]. At this juncture we would like to briefly give some further context on SAT-encodings.…”

Section: Related Workmentioning

confidence: 99%

“…This approach was pioneered by Samer and Veith [34] for treewidth. Their encoding was further expanded on in subsequent works [1,2] and today it still remains one of the most efficient methods for computing optimal tree decompositions. SAT-encodings have also been developed for other graph parameters, including clique-width [18], branchwidth [25], as well as pathwidth and special treewidth [26].…”

Section: Introductionmentioning

confidence: 99%

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SAT-Encodings for Treecut Width and Treedepth

Ganian¹,

Lodha²,

Ordyniak³

et al. 2019

2019 Proceedings of the Twenty-First Workshop on Algorithm Engineering and Experiments (ALENEX)

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The decomposition of graphs is a prominent algorithmic task with numerous applications in computer science. A graph decomposition method is typically associated with a width parameter (such as treewidth) that indicates how well the given graph can be decomposed. Many hard (even #P-hard) algorithmic problems can be solved efficiently if a decomposition of small width is provided; the runtime, however, typically depends exponentially on the decomposition width. Finding an optimal decomposition is itself an NP-hard task. In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research community as they offer the algorithmic advantage over treewidth by supporting so-called fixed-parameter algorithms for certain problems that are not fixed-parameter tractable with respect to treewidth. However, the existing research has mostly been theoretical. A main obstacle for any practical or experimental use of these two width parameters is the lack of any practical or implemented algorithm for actually computing the associated decompositions. We address this obstacle by providing the first practical decomposition algorithms.Our approach for computing treecut width and treedepth decompositions is based on efficient encodings of these decomposition methods to the propositional satisfiability problem (SAT). Once an encoding is generated, any satisfiability solver can be used to find the decomposition. This allows us to leverage the surprising power of todays state-of-the art SAT solvers. The success of SAT-based decomposition methods crucially depends on the used characterisation of the decomposition method, as not every characterisation is suitable for that task. For instance, the successful leading SAT encoding for treewidth is based on a characterisation of treewidth in terms of elimination orderings. For treecut width and treedepth, however, we propose new characterisations that are based on sequences of partitions of the vertex set, a method that was pioneered for clique-width. We implemented and systematically tested our encodings on various benchmark instances, including famous named graphs and random graphs of various density. It turned out that for the

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Section: Methodsmentioning

confidence: 99%

Section: Treecut Widthmentioning

confidence: 96%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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SAT-Encodings for Treecut Width and Treedepth

Ganian¹,

Lodha²,

Ordyniak³

et al. 2019

2019 Proceedings of the Twenty-First Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…It is used in a wide field of applications, such as planning and scheduling [3,22,19], the verification of hardware and software [17], computation of tree decompositions [13,11]. For example, it can be effectively used to design optimal sorting networks [24] or solve the pythagorean triple problem [35].…”

Section: Introductionmentioning

confidence: 99%

Tuning Parallel SAT Solvers

Ehlers¹,

Nowotka²

2018

EasyChair Preprints

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In this paper we present new implementation details and benchmarking results for our parallel portfolio solver TopoSAT2. In particular, we discuss ideas and implementation details for the exchange of learned clauses in a massively-parallel SAT solver which is designed to run more that 1, 000 solver threads in parallel. Furthermore, we go back to the roots of portfolio SAT solving, and discuss the impact of diversifying the solver by using different restart-, branching-and clause database management heuristics. We show that these techniques can be used to tune the solver towards different problems. However, in a case study on formulas derived from Bounded Model Checking problems we see the best performance when using a rather simple clause exchange strategy. We show details of these tests and discuss possible explanations for this phenomenon.As computing times on massively-parallel clusters are expensive, we consider it especially interesting to share these kind of experimental results.

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