Portfolios of Subgraph Isomorphism Algorithms

Kotthoff, Lars; McCreesh, Ciaran; Solnon, Christine

doi:10.1007/978-3-319-50349-3_8

Cited by 30 publications

(32 citation statements)

References 25 publications

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“…In this case, we may gather all solvers in a portfolio, and use an algorithm selection approach to dynamically select from the portfolio the solver which is expected to perform best for each new SI instance to solve, as proposed by Kotthoff et al in [14].…”

Section: Combining Solvers To Take the Best Of Themmentioning

confidence: 99%

Experimental Evaluation of Subgraph Isomorphism Solvers

Solnon

2019

Lecture Notes in Computer Science

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Subgraph Isomorphism (SI) is an NP-complete problem which is at the heart of many structural pattern recognition tasks as it involves finding a copy of a pattern graph into a target graph. In the pattern recognition community, the most well-known SI solvers are VF2, VF3, and RI. SI is also widely studied in the constraint programming community, and many constraint-based SI solvers have been proposed since Ullman, such as LAD and Glasgow, for example. All these SI solvers can solve very quickly some large SI instances, that involve graphs with thousands of nodes. However, McCreesh et al. have recently shown how to randomly generate SI instances the hardness of which can be controlled and predicted, and they have built small instances which are computationally challenging for all solvers. They have also shown that some small instances, which are predicted to be easy and are easily solved by constraint-based solvers, appear to be challenging for VF2 and VF3. In this paper, we widen this study by considering a large test suite coming from eight benchmarks. We show that, as expected for an NP-complete problem, the solving time of an instance does not depend on its size, and that some small instances coming from real applications are not solved by any of the considered solvers. We also show that, if RI and VF3 can solve very quickly a large number of easy instances, for which Glasgow or LAD need more time, they fail at solving some other instances that are quickly solved by Glasgow or LAD, and they are clearly outperformed by Glasgow on hard instances. Finally, we show that we can easily combine solvers to take benefit of their complementarity.This work has been done in collaboration with Ciaran McCreesh, Patrick Prosser, and James Trimble. In particular, all experiments have been run by Ciaran McCreesh and used the Cirrus UK National Tier-2 HPC Service at EPCC (http://www.cirrus.ac.uk) funded by the University of Edinburgh and EPSRC (EP/P020267/1).

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Section: Combining Solvers To Take the Best Of Themmentioning

confidence: 99%

Experimental Evaluation of Subgraph Isomorphism Solvers

Solnon

2019

Lecture Notes in Computer Science

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“…3), hard instances for our algorithm concentrate in the "upper right corner" of the diagram, which contains dense graphs with naturally large treewidth. Therefore, it seems that our algorithm complements the portfolio of algorithms studied by Kotthoff et al [20] by an algorithm suitable just below the phase transition (in view of Fig. 2).…”

Section: Erdős-rényi Graph Setupmentioning

confidence: 57%

“…Our aim is to make step towards competitive implementation of color coding based algorithm for SubEnum, in order to see, where this approach can be potentially beneficial against the existing algorithms. To this end, we extend the comparisons of SubEnum algorithms [9,20,25] to color coding based algorithms, including the one proposed in this paper.…”

Section: Related Workmentioning

confidence: 99%

Efficient Implementation of Color Coding Algorithm for Subgraph Isomorphism Problem

Malík

Suchý

Valla

2019

Lecture Notes in Computer Science

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We consider the subgraph isomorphism problem where, given two graphs G (source graph) and F (pattern graph), one is to decide whether there is a (not necessarily induced) subgraph of G isomorphic to F . While many practical heuristic algorithms have been developed for the problem, as pointed out by McCreesh et al. [JAIR 2018], for each of them there are rather small instances which they cannot cope. Therefore, developing an alternative approach that could possibly cope with these hard instances would be of interest.A seminal paper by Alon, Yuster and Zwick [J. ACM 1995] introduced the color coding approach to solve the problem, where the main part is a dynamic programming over color subsets and partial mappings. As with many exponential-time dynamic programming algorithms, the memory requirements constitute the main limiting factor for its usage. Because these requirements grow exponentially with the treewidth of the pattern graph, all existing implementations based on the color coding principle restrict themselves to specific pattern graphs, e.g., paths or trees. In contrast, we provide an efficient implementation of the algorithm significantly reducing its memory requirements so that it can be used for pattern graphs of larger treewidth. Moreover, our implementation not only decides the existence of an isomorphic subgraph, but it also enumerates all such subgraphs (or given number of them).We provide an extensive experimental comparison of our implementation to other available solvers for the problem.

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“…[2016] (CP-FC in the unlabelled cases, and CP-MAC in the labelled cases, using both branching and filtering for connected subgraphs), the clique encodings of McCreesh et al [2016], and the k↓ algorithm of Hoffmann et al [2017] (which only supports unlabelled, undirected, unconnected instances). Each of these comparator programs is an optimised, dedicated implementation and does not use a general-purpose constraint programming toolkit.…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…Large subgraph isomorphism instances We also ran the algorithms on a set of 5,725 larger instances used in recent studies of subgraph isomorphism [Kotthoff et al, 2016] and maximum common subgraph [Hoffmann et al, 2017]. This benchmark set includes real-world graphs and graphs generated using random models.…”

Section: Experimental Evaluationmentioning

confidence: 99%

A Partitioning Algorithm for Maximum Common Subgraph Problems

McCreesh

Prosser

Trimble

2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

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We introduce a new branch and bound algorithm for the maximum common subgraph and maximum common connected subgraph problems which is based around vertex labelling and partitioning. Our method in some ways resembles a traditional constraint programming approach, but uses a novel compact domain store and supporting inference algorithms which dramatically reduce the memory and computation requirements during search, and allow better dual viewpoint ordering heuristics to be calculated cheaply. Experiments show a speedup of more than an order of magnitude over the state of the art, and demonstrate that we can operate on much larger graphs without running out of memory.

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Portfolios of Subgraph Isomorphism Algorithms

Cited by 30 publications

References 25 publications

Experimental Evaluation of Subgraph Isomorphism Solvers

Experimental Evaluation of Subgraph Isomorphism Solvers

Efficient Implementation of Color Coding Algorithm for Subgraph Isomorphism Problem

A Partitioning Algorithm for Maximum Common Subgraph Problems

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