Abstract
Subgraph isomorphism is a computationally challenging problem with important practical applications, for example in computer vision, biochemistry, and model checking. There are a number of state-of-the-art algorithms for solving the problem, each of which has its own performance characteristics. As with many other hard problems, the single best choice of algorithm overall is rarely the best algorithm on an instance-by-instance. We develop an algorithm selection approach which leverages novel features to characterise subgraph isomorphism problems and dynamically decides which algorithm to use on a per-instance basis. We demonstrate substantial performance improvements on a large set of hard benchmark problems. In addition, we show how algorithm selection models can be leveraged to gain new insights into what affects the performance of an algorithm.
L. Kotthoff – This work was supported by an NSERC E.W.R. Steacie Fellowship and under the NSERC Discovery Grant Program.
C. McCreesh– This work was supported by the Engineering and Physical Sciences Research Council (grant number EP/K503058/1).
C. Solnon – This work has been supported by the ANR project SoLStiCe (ANR-13-BS02-0002-01).
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References
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, Heidelberg (2014). doi:10.1007/978-3-319-10428-7_12. http://dx.doi.org/10.1007/978-3-319-10428-7_12
Battiti, R., Mascia, F.: An algorithm portfolio for the sub-graph isomorphism problem. In: Stützle, T., Birattari, M., Hoos, H.H. (eds.) SLS 2007. LNCS, vol. 4638, pp. 106–120. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74446-7_8
Bischl, B., Kerschke, P., Kotthoff, L., Lindauer, M.T., Malitsky, Y., Fréchette, A., Hoos, H.H., Hutter, F., Leyton-Brown, K., Tierney, K., Vanschoren, J.: ASlib: a benchmark library for algorithm selection. Artif. Intell. J. (2016, in press)
Cohen, W.W.: Fast effective rule induction. In: Twelfth International Conference on Machine Learning, pp. 115–123. Morgan Kaufmann (1995)
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). http://doi.ieeecomputersociety.org/10.1109/TPAMI.2004.75
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). http://dx.doi.org/10.1016/S0167-8655(02)00253–2
Giugno, R., Bonnici, V., Bombieri, N., Pulvirenti, A., Ferro, A., Shasha, D.: Grapes: a software for parallel searching on biological graphs targeting multi-core architectures. PLoS ONE 8(10), e76911 (2013). http://dx.doi.org/10.1371%2Fjournal.pone.0076911
Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1–2), 43–62 (2001)
Huberman, B.A., Lukose, R.M., Hogg, T.: An economics approach to hard computational problems. Science 275(5296), 51–54 (1997)
Kotthoff, L.: LLAMA: Leveraging learning to automatically manage algorithms. Technical report arXiv:1306.1031 June 2003
Kotthoff, L.: Algorithm selection for combinatorial search problems: a survey. AI Mag. 35(3), 48–60 (2014)
Kotthoff, L., Kerschke, P., Hoos, H., Trautmann, H.: Improving the state of the art in inexact TSP solving using per-instance algorithm selection. In: Dhaenens, C., Jourdan, L., Marmion, M.-E. (eds.) LION 2015. LNCS, vol. 8994, pp. 202–217. Springer, Heidelberg (2015). doi:10.1007/978-3-319-19084-6_18
Larrosa, J., Valiente, G.: Constraint satisfaction algorithms for graph pattern matching. Math. Struct. Compt. 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, Heidelberg (2015). doi:10.1007/978-3-319-23219-5_21. http://dx.doi.org/10.1007/978-3-319-23219-5_21
McCreesh, C., Prosser, P., Trimble, J.: Heuristics and really hard instances for subgraph isomorphism problems. In: IJCAI (2016, to appear)
McGregor, J.J.: Relational consistency algorithms and their application in finding subgraph and graph isomorphisms. Inf. Sci. 19(3), 229–250 (1979)
Mohr, R., Henderson, T.: Arc and path consistency revisited. Artif. Intell. 28, 225–233 (1986)
O’Mahony, E., Hebrard, E., Holland, A., Nugent, C., O’Sullivan, B.: Using case-based reasoning in an algorithm portfolio for constraint solving. In: Proceedings of the 19th Irish Conference on Artificial Intelligence and Cognitive Science, January 2008
Régin, J.C.: A filtering algorithm for constraints of difference in CSPs. In: Proceeding of the 12th Conference American Association Artificial Intelligence, vol. 1, pp. 362–367. American Association Artificial Intelligence (1994)
Rice, J.R.: The algorithm selection problem. Adv. Comput. 15, 65–118 (1976)
Sabharwal, A., Samulowitz, H.: Insights into parallelism with intensive knowledge sharing. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 655–671. Springer, Heidelberg (2014). doi:10.1007/978-3-319-10428-7_48. http://dx.doi.org/10.1007/978-3-319-10428-7_12
Seipp, J., Braun, M., Garimort, J., Helmert, M.: Learning portfolios of automatically tuned planners. In: ICAPS (2012)
Sevegnani, M., Calder, M.: Bigraphs with sharing. Theor. Comput. Sci. 577, 43–73 (2015). http://www.sciencedirect.com/science/article/pii/S0304397515001085
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)
Solnon, C.: Alldifferent-based filtering for subgraph isomorphism. Artif. Intell. 174(12–13), 850–864 (2010). http://dx.doi.org/10.1016/j.artint.2010.05.002
Ullmann, J.R.: An algorithm for subgraph isomorphism. J. ACM 23(1), 31–42 (1976)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: Portfolio-based algorithm selection for SAT. J. Artif. Intell. Res. (JAIR) 32, 565–606 (2008)
Zampelli, S., Deville, Y., Solnon, C.: Solving subgraph isomorphism problems with constraint programming. Constraints 15(3), 327–353 (2010)
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Kotthoff, L., McCreesh, C., Solnon, C. (2016). Portfolios of Subgraph Isomorphism Algorithms. In: Festa, P., Sellmann, M., Vanschoren, J. (eds) Learning and Intelligent Optimization. LION 2016. Lecture Notes in Computer Science(), vol 10079. Springer, Cham. https://doi.org/10.1007/978-3-319-50349-3_8
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