Abstract
Effective search for graph automorphisms allows identifying symmetries in many discrete structures, ranging from chemical molecules to microprocessor circuits. Using this type of structure can enhance visualization as well as speed up computational optimization and verification. Competitive algorithms for the graph automorphism problem are based on efficient partition refinement augmented with group-theoretic pruning techniques. In this paper, we improve prior algorithms for the graph automorphism problem by introducing simultaneous refinement of multiple partitions, which enables the anticipation of future conflicts in search and leads to significant pruning, reducing overall runtimes. Empirically, we observe an exponential speedup for the family of Miyazaki graphs, which have been shown to impede leading graph-automorphism algorithms.
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References
ISPD (2005), http://archive.sigda.org/ispd2005/contest.htm
Aloul, F.A., Markov, I.L., Sakallah, K.A.: Shatter: Efficient symmetry-breaking for boolean satisfiability. In: Proc. 40th IEEE/ACM Design Automation Conference (DAC), Anaheim, California, pp. 836–839 (2003)
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult sat instances in the presence of symmetry. In: Proc. 39th IEEE/ACM Design Automation Conference (DAC), New Orleans, Louisiana, pp. 731–736 (2002)
binary networks, https://sites.google.com/site/santofortunato/inthepress2
bliss 0.72 (2011), http://www.tcs.hut.fi/Software/bliss/bliss-0.72.zip
U. S. Census Bureau, http://www.census.gov/geo/www/tiger/tigerua/ua_tgr2k.html.
Cheswick, B., Burch, H., Branigan, S.: Mapping and visualizing the internet. In: USENIX Annual Technical Conference, pp. 1–13 (2000)
SAT Competition, http://www.satcompetition.org
Darga, P.T., Liffiton, M.H., Sakallah, K.A., Markov, I.L.: Exploiting structure in symmetry detection for CNF. In: Proc. 41st IEEE/ACM Design Automation Conference (DAC), San Diego, California, pp. 530–534 (2004)
Darga, P.T., Sakallah, K.A., Markov, I.L.: Faster symmetry discovery using sparsity of symmetries. In: Proc. 45th IEEE/ACM Design Automation Conference (DAC), Anaheim, California, pp. 149–154 (2008)
Fraleigh, J.B.: A First Course in Abstract Algebra, 6th edn. Addison Wesley Longman, Reading (2000)
Govindan, R., Tangmunarunkit, H.: Heuristics for internet map discovery. In: IEEE INFOCOM, pp. 1371–1380 (2000)
Junttila, T., Kaski, P.: Engineering an efficient canonical labeling tool for large and sparse graphs. In: Ninth Workshop on Algorithm Engineering and Experiments (ALENEX 2007), New Orleans, LA (2007)
Junttila, T., Kaski, P.: Conflict Propagation and Component Recursion for Canonical Labeling. In: Marchetti-Spaccamela, A., Segal, M. (eds.) TAPAS 2011. LNCS, vol. 6595, pp. 151–162. Springer, Heidelberg (2011)
Kaski, P.: http://www.tcs.hut.fi/Software/bliss/benchmarks/index.shtml
Katebi, H., Sakallah, K.A., Markov, I.L.: Symmetry and satisfiability: An update. In: Proc. Satisfiability Symposium (SAT), Edinburgh, Scotland (2010)
Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. E 80, 016118 (2009)
McKay, B.D.: nauty user’s guide (version 2.2), http://cs.anu.edu.au/~bdm/nauty/nug.pdf
Brendan, D.: McKay. Practical graph isomorphism. Congressus Numerantium 30, 45–87 (1981)
Miyazaki, T.: The complexity of McKay’s canonical labeling algorithm, p. 239. Amer. Mathematical Society (1997)
nishe 0.1., http://gregtener.com/media/upload/nishe-0.1.tar.bz2
Tener, G., Deo, N.: Efficient isomorphism of miyazaki graphs. In: 39th Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL (2008)
Velev, M.N., Bryant, R.E.: Effective use of boolean satisfiability procedures in the formal verification of superscalar and vliw microprocessors. In: Proc. Design Automation Conference (DAC), New Orleans, Louisiana, pp. 226–231 (2001)
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Katebi, H., Sakallah, K.A., Markov, I.L. (2012). Conflict Anticipation in the Search for Graph Automorphisms. In: Bjørner, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2012. Lecture Notes in Computer Science, vol 7180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28717-6_20
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DOI: https://doi.org/10.1007/978-3-642-28717-6_20
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