We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on the vertex set, which are cost, capacity, and demand. The objective of this problem is to compute a demand assignment of least cost, such that the demand of each vertex is fully-assigned to some of its closed neighbours without exceeding the amount of capacity they provide. In this paper, we provide the first constant factor approximation for this problem on planar graphs, based on a new perspective on the hierarchical structure of outer-planar graphs. We believe that this new perspective and technique can be applied to other capacitated covering problems to help tackle vertices of large degrees. © 2011 Springer-Verlag.
CITATION STYLE
Kao, M. J., & Lee, D. T. (2011). Capacitated domination: Constant factor approximations for planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7074 LNCS, pp. 494–503). https://doi.org/10.1007/978-3-642-25591-5_51
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