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Approximation Algorithms for the Capacitated Domination Problem

  • Mong-Jen Kao
  • Han-Lin Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6213)

Abstract

We consider the Capacitated Domination problem, which models a service-requirement assignment scenario and is a generalization to the well-known Dominating Set problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service.

In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to different demand assignment models on general graphs. On the other hand, from the perspective of parameterization, we prove that this problem is W[1]-hard when parameterized by a structure of the graph called treewidth. Based on this hardness result, we present exact fixed-parameter tractable algorithms with respect to treewidth and maximum capacity of the vertices. This algorithm is further extended to obtain pseudo-polynomial time approximation schemes for planar graphs.

Keywords

Approximation Algorithm Planar Graph Vertex Cover Demand Model Input Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mong-Jen Kao
    • 1
  • Han-Lin Chen
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaiwan

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