Capacitated Domination Problem

  • Authors:

  • Mong-Jen Kao;Chung-Shou Liao;D. T. Lee

  • Affiliations:

  • National Taiwan University, Department of Computer Science and Information Engineering, Taipei, Taiwan;National Taiwan University, Department of Computer Science and Information Engineering, Taipei, Taiwan and Academia Sinica, Institute of Information Science, Nankang, 115, Taipei, Taiwan;National Taiwan University, Department of Computer Science and Information Engineering, Taipei, Taiwan and Academia Sinica, Institute of Information Science, Nankang, 115, Taipei, Taiwan

  • Venue:
  • Algorithmica
  • Year:
  • 2011

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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.