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Sequential and Parallel Solution-Biased Search for Subgraph Algorithms

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11494))

Abstract

The current state of the art in subgraph isomorphism solving involves using degree as a value-ordering heuristic to direct backtracking search. Such a search makes a heavy commitment to the first branching choice, which is often incorrect. To mitigate this, we introduce and evaluate a new approach, which we call “solution-biased search”. By combining a slightly-random value-ordering heuristic, rapid restarts, and nogood recording, we design an algorithm which instead uses degree to direct the proportion of search effort spent in different subproblems. This increases performance by two orders of magnitude on satisfiable instances, whilst not affecting performance on unsatisfiable instances. This algorithm can also be parallelised in a very simple but effective way: across both satisfiable and unsatisfiable instances, we get a further speedup of over thirty from thirty-six cores, and over one hundred from ten distributed-memory hosts. Finally, we show that solution-biased search is also suitable for optimisation problems, by using it to improve two maximum common induced subgraph algorithms.

This work was supported by the Engineering and Physical Sciences Research Council (grant numbers EP/P026842/1, EP/M508056/1, and EP/N007565). This work 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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Notes

  1. 1.

    https://github.com/ciaranm/glasgow-subgraph-solver/.

  2. 2.

    It may be possible to further improve the solver by also introducing randomness or some form of learning into its variable-ordering heuristic. However, simultaneously introducing a second change would considerably complicate the empirical analysis. Additionally, the solver’s current hand-crafted variable-ordering heuristics already beat adaptive heuristics like impact or activity-based search.

  3. 3.

    For solving a counting or enumeration problem, matters become slightly more complicated, but not devastatingly so.

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Acknowledgements

The authors would like to thank Özgür Akgün, Chris Jefferson, Sonja Kraiczy, Christophe Lecoutre, Christine Solnon, and Craig Reilly for their comments.

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Authors and Affiliations

  1. University of Glasgow, Glasgow, Scotland

    Blair Archibald, Ciaran McCreesh, Patrick Prosser & James Trimble

  2. University of St Andrews, St Andrews, Scotland

    Fraser Dunlop & Ruth Hoffmann

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  1. Blair Archibald
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  2. Fraser Dunlop
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  3. Ruth Hoffmann
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Correspondence to Ciaran McCreesh .

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Editors and Affiliations

  1. Ecole Polytechnique de Montréal, Montréal, QC, Canada

    Louis-Martin Rousseau

  2. University of Western Macedonia, Kozani, Greece

    Kostas Stergiou

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Archibald, B., Dunlop, F., Hoffmann, R., McCreesh, C., Prosser, P., Trimble, J. (2019). Sequential and Parallel Solution-Biased Search for Subgraph Algorithms. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_2

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