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A heuristic approach for dividing graphs into bi-connected components with a size constraint

Author

Listed:
  • Raka Jovanovic

    (Hamad bin Khalifa University)

  • Tatsushi Nishi

    (Osaka University)

  • Stefan Voß

    (University of Hamburg
    Pontificia Universidad Católica de Valparaíso)

Abstract

In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on the open ear decomposition of graphs. Its essential part is an adaptation of the breadth first search which makes it possible to grow bi-connected subgraphs. The proposed randomized algorithm consists of growing several subgraphs in parallel. The quality of solutions generated in this way is further improved using a local search which exploits neighboring relations between the subgraphs. In order to evaluate the performance of the method, an algorithm for generating pseudo-random unit disc graphs with known optimal solutions is created. Computational experiments have also been conducted on graphs representing electrical distribution systems for the real-world problem of dividing them into a system of fault tolerant interconnected microgrids. The experiments show that the proposed method frequently manages to find optimal solutions and has an average error of only a few percent to known optimal solutions. Further, it manages to find high quality approximate solutions for graphs having up to 10,000 nodes in reasonable time.

Suggested Citation

  • Raka Jovanovic & Tatsushi Nishi & Stefan Voß, 2017. "A heuristic approach for dividing graphs into bi-connected components with a size constraint," Journal of Heuristics, Springer, vol. 23(2), pages 111-136, June.
    • Handle: RePEc:spr:joheur:v:23:y:2017:i:2:d:10.1007_s10732-017-9331-3
    DOI: 10.1007/s10732-017-9331-3
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    References listed on IDEAS

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    1. Goldschmidt, Olivier & Takvorian, Alexis & Yu, Gang, 1996. "On finding a biconnected spanning planar subgraph with applications to the facilities layout problem," European Journal of Operational Research, Elsevier, vol. 94(1), pages 97-105, October.
    2. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    3. Austin Buchanan & Je Sang Sung & Sergiy Butenko & Eduardo L. Pasiliao, 2015. "An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 178-188, February.
    4. Bazgan, Cristina & Tuza, Zsolt & Vanderpooten, Daniel, 2010. "Satisfactory graph partition, variants, and generalizations," European Journal of Operational Research, Elsevier, vol. 206(2), pages 271-280, October.
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