Using Canonical Codes to Efficiently Solve the Benzenoid Generation Problem with Constraint Programming

Peng, Xiao; Solnon, Christine

doi:10.4230/LIPIcs.CP.2023.28

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LIPIcs.CP.2023.28.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.CP.2023.28
URN: urn:nbn:de:0030-drops-190650

Author Details

Xiao Peng

Univ Lyon, INSA Lyon, Inria, CITI, EA3720, 69621 Villeurbanne, France

Christine Solnon

Univ Lyon, INSA Lyon, Inria, CITI, EA3720, 69621 Villeurbanne, France

Acknowledgements

We want to thank authors of [Yannick Carissan et al., 2021] who helped us reproduce their results.

Cite AsGet BibTex

Xiao Peng and Christine Solnon. Using Canonical Codes to Efficiently Solve the Benzenoid Generation Problem with Constraint Programming. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CP.2023.28

Abstract

The Benzenoid Generation Problem (BGP) aims at generating all benzenoid molecules that satisfy some given properties. This problem has important applications in chemistry, and Carissan et al (2021) have shown us that Constraint Programming (CP) is well suited for modelling this problem because properties defined by chemists are easy to express by means of constraints. Benzenoids are described by hexagon graphs and a key point for an efficient enumeration of these graphs is to be invariant to rotations and symmetries. In this paper, we introduce canonical codes that uniquely characterise hexagon graphs while being invariant to rotations and symmetries. We show that these codes may be defined by means of constraints. We also introduce a global constraint for ensuring that codes are canonical, and a global constraint for ensuring that a pattern is included in a code. We experimentally compare our new CP model with the CP-based approach of Carissan et al (2021), and we show that it has better scale-up properties.

Subject Classification

ACM Subject Classification

Mathematics of computing → Graph enumeration
Computing methodologies → Artificial intelligence

Keywords

Benzenoid Generation Problem
Canonical Code
Hexagon Graph

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References

Gunnar Brinkmann, Gilles Caporossi, and Pierre Hansen. A constructive enumeration of fusenes and benzenoids. J. Algorithms, 45(2):155-166, 2002.
Yannick Carissan, Denis Hagebaum-Reignier, Nicolas Prcovic, Cyril Terrioux, and Adrien Varet. Using constraint programming to generate benzenoid structures in theoretical chemistry. In Helmut Simonis, editor, Principles and Practice of Constraint Programming - 26th International Conference, CP, volume 12333 of Lecture Notes in Computer Science, pages 690-706. Springer, 2020.
Yannick Carissan, Denis Hagebaum-Reignier, Nicolas Prcovic, Cyril Terrioux, and Adrien Varet. Exhaustive generation of benzenoid structures sharing common patterns. In Laurent D. Michel, editor, 27th International Conference on Principles and Practice of Constraint Programming, CP, volume 210 of LIPIcs, pages 19:1-19:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.
Yannick Carissan, Denis Hagebaum-Reignier, Nicolas Prcovic, Cyril Terrioux, and Adrien Varet. How constraint programming can help chemists to generate benzenoid structures and assess the local aromaticity of benzenoids. Constraints An Int. J., 27(3):192-248, 2022.
S. J. Cyvin, J. Brunvoll, and B. N. Cyvin. Search for concealed non-kekulean benzenoids and coronoids. Journal of Chemical Information and Computer Sciences, 29(4):236-244, 1989.
Romain Deville, Élisa Fromont, Baptiste Jeudy, and Christine Solnon. Grima: A grid mining algorithm for bag-of-grid-based classification. In Antonio Robles-Kelly, Marco Loog, Battista Biggio, Francisco Escolano, and Richard C. Wilson, editors, Structural, Syntactic, and Statistical Pattern Recognition - Joint IAPR International Workshop, S+SSPR, Proceedings, volume 10029 of Lecture Notes in Computer Science, pages 132-142, 2016.
Romain Deville, Élisa Fromont, Baptiste Jeudy, and Christine Solnon. Mining frequent patterns in 2d+t grid graphs for cellular automata analysis. In Pasquale Foggia, Cheng-Lin Liu, and Mario Vento, editors, Graph-Based Representations in Pattern Recognition - 11th IAPR-TC-15 International Workshop, GbRPR 2017, Anacapri, Italy, May 16-18, 2017, Proceedings, volume 10310 of Lecture Notes in Computer Science, pages 177-186, 2017.
Stéphane Gosselin, Guillaume Damiand, and Christine Solnon. Efficient search of combinatorial maps using signatures. Theor. Comput. Sci., 412(15):1392-1405, 2011.
Brendan D. McKay and Adolfo Piperno. Practical graph isomorphism, II. J. Symb. Comput., 60:94-112, 2014.
Siegfried Nijssen and Joost N. Kok. The gaston tool for frequent subgraph mining. In Proceedings of the 2nd International Workshop on Graph-Based Tools, GraBaTs 2004, Rome, Italy, October 2, 2004, volume 127 of Electronic Notes in Theoretical Computer Science, pages 77-87. Elsevier, 2004. URL: https://doi.org/10.1016/j.entcs.2004.12.039.
C. Prud'homme, J.-G. Fages, and X. Lorca. Choco Documentation. TASC, INRIA Rennes, LINA CNRS UMR 6241, COSLING S.A.S., 2016. URL: http://www.choco-solver.org.
Xifeng Yan and Jiawei Han. gspan: graph-based substructure pattern mining. In 2002 IEEE International Conference on Data Mining, 2002. Proceedings., pages 721-724, 2002. URL: https://doi.org/10.1109/ICDM.2002.1184038.