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Capacitated Domination Problem

Algorithmica volume 60, pages 274–300 (2011)Cite this article

Abstract

We consider a generalization of the well-known domination problem on graphs. The (soft) capacitated domination problem with demand constraints is to find a dominating set D of minimum cardinality satisfying both the capacity and demand constraints. The capacity constraint specifies that each vertex has a capacity that it can use to meet the demands of dominated vertices in its closed neighborhood, and the number of copies of each vertex allowed in D is unbounded. The demand constraint specifies the demand of each vertex in V to be met by the capacities of vertices in D dominating it. In this paper, we study the capacitated domination problem on trees from an algorithmic point of view. We present a linear time algorithm for the unsplittable demand model, and a pseudo-polynomial time algorithm for the splittable demand model. In addition, we show that the capacitated domination problem on trees with splittable demand constraints is NP-complete (even for its integer version) and provide a polynomial time approximation scheme (PTAS). We also give a primal-dual approximation algorithm for the weighted capacitated domination problem with splittable demand constraints on general graphs.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan

    Mong-Jen Kao, Chung-Shou Liao & D. T. Lee

  2. Institute of Information Science, Academia Sinica, Nankang, Taipei, 115, Taiwan

    Chung-Shou Liao & D. T. Lee

Authors
  1. Mong-Jen Kao
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  2. Chung-Shou Liao
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  3. D. T. Lee
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Corresponding author

Correspondence to Chung-Shou Liao.

Additional information

An extended abstract of this paper appeared in the 18th International Symposium on Algorithms and Computation (ISAAC), pp. 256–267, 2007.

Supported in part by the National Science Council under the Grants NSC95-2221-E-001-016-MY3, NSC96-2752-E-002-005-PAE, NSC96-2217-E-001-001, NSC96-3114-P-001-002-Y, and NSC96-3114-P-001-007.

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Kao, MJ., Liao, CS. & Lee, D.T. Capacitated Domination Problem. Algorithmica 60, 274–300 (2011). https://doi.org/10.1007/s00453-009-9336-x

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  • DOI: https://doi.org/10.1007/s00453-009-9336-x

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