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 demand of dominated vertices in its closed neighborhood, and the number of copies of each vertex allowed in D is unbounded. The demand constraint specifies that the demand of each vertex in V is met by the capacities of vertices in D dominating it. In this paper, we study the capacitated domination problem on trees. 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 \(\frac{3}{2}\)-approximation algorithm. We also give a primal-dual approximation algorithm for the weighted capacitated domination problem with splittable demand constraints on general graphs.
Supported in part by the National Science Council under the Grants NSC95-2221-E-001-016-MY3, NSC-94-2422-H-001-0001, and NSC-95-2752-E-002-005-PAE, and by the Taiwan Information Security Center (TWISC) under the Grants NSC NSC95-2218-E-001-001, NSC95-3114-P-001-002-Y, NSC94-3114-P-001-003-Y and NSC 94-3114-P-011-001.
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Kao, M.-J., Liao, C.S., Lee, D.T.: Capacitated domination problem, manuscript (September 2007), http://www.iis.sinica.edu.tw/~shou794/research/CDS_200709.pdf
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Kao, MJ., Liao, CS. (2007). Capacitated Domination Problem. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_24
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DOI: https://doi.org/10.1007/978-3-540-77120-3_24
Publisher Name: Springer, Berlin, Heidelberg
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