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An improved binary programming formulation for the secure domination problem

Author

Listed:
  • Ryan Burdett

    (Flinders University)

  • Michael Haythorpe

    (Flinders University)

Abstract

The secure domination problem, a variation of the domination problem with some important real-world applications, is considered. Very few algorithmic attempts to solve this problem have been presented in literature, and the most successful to date is a binary programming formulation which is solved using CPLEX. A new binary programming formulation is proposed here which requires fewer constraints and fewer binary variables than the existing formulation. It is implemented in CPLEX, and tested on certain families of graphs that have previously been considered in the context of secure domination. It is shown that the runtime required for the new formulation to solve the instances is significantly less than that of the existing formulation. An extension of our formulation that solves the related, but further constrained, secure connected domination problem is also given; to the best of the authors’ knowledge, this is the first such formulation in literature.

Suggested Citation

  • Ryan Burdett & Michael Haythorpe, 2020. "An improved binary programming formulation for the secure domination problem," Annals of Operations Research, Springer, vol. 295(2), pages 561-573, December.
    • Handle: RePEc:spr:annopr:v:295:y:2020:i:2:d:10.1007_s10479-020-03810-6
    DOI: 10.1007/s10479-020-03810-6
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    References listed on IDEAS

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    1. D. Pradhan & Anupriya Jha, 2018. "On computing a minimum secure dominating set in block graphs," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 613-631, February.
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