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Solving the minimum-cost double Roman domination problem

Author

Listed:
  • Ana Klobučar Barišić

    (University of Zagreb)

  • Robert Manger

    (Faculty of Science, University of Zagreb)

Abstract

Double Roman domination (DRD) is a combinatorial optimization problem posed on undirected graphs. It can be interpreted as allocating certain service providers (e.g., military formations, fire brigades or ambulances) to chosen locations within a certain area. Thereby the whole service (i.e., response to enemy attacks, fire or medical urgencies) should be established in a least expensive way, while still assuring a required “double Roman” level of availability and redundancy of providers. The standard version of DRD treated in the literature identifies the total expense of service with the total number of needed providers. In this paper a new “minimum-cost” version of DRD is considered, which is more general and more realistic than the standard version. It takes into account the fact that the actual expenses of providing service can differ from one location to another. Thus, formally speaking, each vertex in our graph is given a cost that is intepreted as the cost of keeping one service provider at the corresponding location. First, it is noted that the considered minimum-cost DRD problem is NP-hard, not only for general graphs but also for many special graph classes. Next, a dynamic programming algorithm is constructed, which shows that the problem can still be solved in linear time if the involved graph is a tree. Finally, as a solution for general graphs, a heuristic is proposed based on greedy construction and local search. Performance of both algorithms is evaluated by experiments.

Suggested Citation

  • Ana Klobučar Barišić & Robert Manger, 2024. "Solving the minimum-cost double Roman domination problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 793-817, September.
  • Handle: RePEc:spr:cejnor:v:32:y:2024:i:3:d:10.1007_s10100-023-00884-y
    DOI: 10.1007/s10100-023-00884-y
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    References listed on IDEAS

    as
    1. Darja Rupnik Poklukar & Janez Žerovnik, 2023. "Double Roman Domination: A Survey," Mathematics, MDPI, vol. 11(2), pages 1-20, January.
    2. S. Banerjee & Michael A. Henning & D. Pradhan, 2020. "Algorithmic results on double Roman domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 90-114, January.
    Full references (including those not matched with items on IDEAS)

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