Recursive-parallel algorithm for solving the graph-subgraph isomorphism problem

V. V. Vasilchikov

Modelirovanie i analiz informacionnyh sistem, Tome 29 (2022) no. 1, pp. 30-43.

Résumé

The paper proposes a parallel algorithm for solving the Graph-Subgraph Isomorphism Problem and makes an experimental study of its efficiency. The problem is one of the most famous NP-complete problems. Its solution may be required when solving many practical problems associated with the study of complex structures. We solve the problem in a formulation that requires finding all existing isomorphic substitutions or proving their absence. In view of the high complexity of the problem, it is natural to want to speed up its solution by parallelizing the algorithm. We used the RPM ParLib library, developed by the author, as the main tool to program the algorithm. This library allows us to develop effective applications for parallel computing on a local network under the control of the runtime environment .NET Framework. Thanks to this library, applications have the ability to generate parallel branches of computation directly during program execution and dynamically redistribute work between computing modules. Any language with support of the .NET Framework can be used as a programming language in conjunction with this library. For the numerical experiment, an open database from the Internet was used, which was specially developed to study algorithms for searching for isomorphic substitutions. Also, the author has developed a special application in C# for generating additional sets of initial data with specified characteristics. The aim of the experiment was to study the speedup achieved due to the recursively parallel organization of computations. The paper provides a detailed description of the proposed algorithm, as well as the results obtained during the experiment.

Détail

Keywords: graph-subgraph isomorphism problem, parallel algorithm, recursion
Mots-clés : .NET.

Bibliographie

[1] M. R. Garey, D. S. Johnson, Computers and intractability: a guide to the theory of NP-completeness, W. H. Freeman and Co, San Francisco, 1979 | MR | Zbl

[2] J. R. Ullmann, “An algorithm for subgraph isomorphism”, Journal of the Association for Computing Machinery, 23:1 (1976), 31–42 | DOI | MR

[3] L. P. Cordella, P. Foggia, C. Sansone, M. Vento, “Performance evaluation of the vf graph matching algorithm”, Proc. of the 10th ICIAP, IEEE Computer SocietyPress, 1999, 1172–1177

[4] L. P. Cordella, P. Foggia, C. Sansone, M. Vento, “An improved algorithm for matching large graphs”, Proc. of the 3rd IAPR-TC-15 international workshop on graph-based representations (Italy, 2001), 149–159 | MR

[5] V. Carletti, P. Foggia, A. Saggese, M. Vento, “Challenging the time complexity of exact subgraph isomorphism for huge and dense graphs with VF3”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 40:4 (2018), 804–818 | DOI

[6] M. B. Il'yashenko, “Unificirovannyj podhod k resheniyu zadach morfizma na grafah”, Elektronnoe modelirovanie, 30:1 (2008), 19–41

[7] M. B. Il'yashenko, “Reshenie zadachi poiska graf-podgraf izomorfizma dlya semanticheskogo analiza specializirovannyh cifrovyh sistem”, Nauchnye trudy DonTU. Seriya “Informatika, kibernetika i vychislitel'naya tekhnika”, 16 (2012), 46–57

[8] J. R. Ullmann, “Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism”, Journal of Experimental Algorithmics, 15:1 (2011), 1–64 | MR

[9] M. B. Il'yashenko, “Razrabotka i issledovanie parallel'nogo algoritma proverki graf-podgraf izomorfizma”, Radioelektronika. Informatika. Upravlenie, 1 (2006), 63–69

[10] V. Carletti, P. Foggia, P. Ritrovato, M. Vento, V. Vigilante \title A parallel algorithm for subgraph isomorphism, International workshop on graph-based representations in pattern recognition, LNCS, 11510, Springer, Cham, 2019, 141–151 | MR

[11] V. V. Vasilchikov, Sredstva parallelnogo programmirovaniya dlya vychislitelnykh sistem s dinamicheskoy balansirovkoy zagruzki, YarGU, Yaroslavl, 2001

[12] V. V. Vasilchikov, Kommunikatsionnyy modul dlya organizatsii polnosvyaznogo soedineniya kompyuterov v lokalnoy seti s ispolzovaniem .NET Framework, Svidetelstvo o gosudarstvennoy registratsii programmy dlya EVM No 2013619925, 2013

[13] V. V. Vasilchikov, Biblioteka podderzhki rekursivno-parallelnogo programmirovaniya dlya .NET Framework, Svidetelstvo o gosudarstvennoy registratsii programmy dlya EVM No 2013619926, 2013 | MR

[14] V. V. Vasilchikov, “On the recursive-parallel programming for the .NET Framework”, Automatic Control and Computer Sciences, 48:7 (2014), 575–580, Springer | DOI

[15] V. V. Vasilchikov, “On optimization and parallelization of the little algorithm for solving the travelling salesman problem”, Automatic Control and Computer Sciences, 51:7 (2017), 551–557 | DOI | MR

[16] V. V. Vasilchikov, “On a recursive-parallel algorithm for solving the knapsack problem”, Automatic Control and Computer Sciences, 52:7 (2018), 810–816 | DOI | MR

[17] V. V. Vasilchikov, “Parallel algorithm for solving the graph isomorphism problem”, Modeling and analysis of information systems, 27:1 (2020), 86–94 | DOI | MR

[18] P. Foggia, C. Sansone, M. Vento, A database of graphs for isomorphism and sub-graph isomorphism benchmarkin, CoRR, 2001 https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.95.6803&rep=rep1&type=pdf