Capacitated domination: constant factor approximations for planar graphs

Authors:
Mong-Jen Kao;D. T. Lee
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

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Abstract

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.