Abstract
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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Notes
- 1.
Glasgow is available at https://github.com/ciaranm/glasgow-subgraph-solver.
References
Archibald, B., Dunlop, F., Hoffmann, R., McCreesh, C., Prosser, P., Trimble, J.: Sequential and parallel solution-biased search for subgraph algorithms. In: 16th International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research (2019)
Audemard, G., Lecoutre, C., Samy-Modeliar, M., Goncalves, G., Porumbel, D.: Scoring-based neighborhood dominance for the subgraph isomorphism problem. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 125–141. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_12
Bombieri, N., Bonnici, V., Giugno, R.: Parallel searching on biological networks. In: 27th Euromicro International Conference on Parallel, Distributed and Network-Based Processing, PDP, pp. 307–314. IEEE (2019)
Bonnici, V., Giugno, R.: On the variable ordering in subgraph isomorphism algorithms. IEEE/ACM Trans. Comput. Biol. Bioinf. 14(1), 193–203 (2017)
Carletti, V., Foggia, P., Saggese, A., Vento, M.: Challenging the time complexity of exact subgraph isomorphism for huge and dense graphs with VF3. IEEE Trans. Pattern Anal. Mach. Intell. 40(4), 804–818 (2018)
Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. In: 12th International Joint Conference on Artificial Intelligence (IJCAI), pp. 331–340 (1991)
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. IJPRAI 18(3), 265–298 (2004)
Cordella, L.P., Foggia, P., Sansone, C., Vento, M.: A (sub)graph isomorphism algorithm for matching large graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26(10), 1367–1372 (2004)
Damiand, G., Solnon, C., de la Higuera, C., Janodet, J.C., Samuel, E.: Polynomial algorithms for subisomorphism of nD open combinatorial maps. Comput. Vis. Image Underst. (CVIU) 115(7), 996–1010 (2011)
De Santo, M., Foggia, P., Sansone, C., Vento, M.: A large database of graphs and its use for benchmarking graph isomorphism algorithms. Pattern Recogn. Lett. 24(8), 1067–1079 (2003)
Erdős, P., Rényi, A.: On random graphs I. Publicationes Mathematicae 6, 290–297 (1959)
Hoffmann, R., et al.: Observations from parallelising three maximum common (connected) subgraph algorithms. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 298–315. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93031-2_22
Knuth, D.E.: The Stanford GraphBase - a platform for combinatorial computing. ACM (1993)
Kotthoff, L., McCreesh, C., Solnon, C.: Portfolios of subgraph isomorphism algorithms. In: Festa, P., Sellmann, M., Vanschoren, J. (eds.) LION 2016. LNCS, vol. 10079, pp. 107–122. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-50349-3_8
Larrosa, J., Valiente, G.: Constraint satisfaction algorithms for graph pattern matching. Math. Struct. Comput. Sci. 12(4), 403–422 (2002)
McCreesh, C., Prosser, P.: A parallel, backjumping subgraph isomorphism algorithm using supplemental graphs. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 295–312. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_21
Mccreesh, C., Prosser, P., Solnon, C., Trimble, J.: When subgraph isomorphism is really hard, and why this matters for graph databases. J. Artif. Intell. Res. 61, 723–759 (2018)
Solnon, C.: AllDifferent-based filtering for subgraph isomorphism. Artif. Intell. 174(12–13), 850–864 (2010)
Solnon, C., Damiand, G., de la Higuera, C., Janodet, J.: On the complexity of submap isomorphism and maximum common submap problems. Pattern Recogn. 48(2), 302–316 (2015)
Ullmann, J.R.: An algorithm for subgraph isomorphism. J. ACM 23(1), 31–42 (1976)
Zampelli, S., Deville, Y., Solnon, C.: Solving subgraph isomorphism problems with constraint programming. Constraints 15(3), 327–353 (2010)
Zampelli, S., Deville, Y., Solnon, C., Sorlin, S., Dupont, P.: Filtering for subgraph isomorphism. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 728–742. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74970-7_51
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Solnon, C. (2019). Experimental Evaluation of Subgraph Isomorphism Solvers. In: Conte, D., Ramel, JY., Foggia, P. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2019. Lecture Notes in Computer Science(), vol 11510. Springer, Cham. https://doi.org/10.1007/978-3-030-20081-7_1
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