Approximation Algorithms for the Capacitated Domination Problem

Details Approximation Algorithms for the Capacitated Domination Problem Approximation Algorithms for the Capacitated Domination Problem

2010-04-16

arxiv.org/abs/1004.2839v2

Computer Science

Discrete Mathematics

Scientific paper

We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em 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 for this problem on general graphs, which also establishes the corresponding approximation results to the well-known approximations of the traditional {\em Dominating Set} problem. Together with our previous work, this closes the problem of generally approximating the optimal solution. On the other hand, from the perspective of parameterization, we prove that this problem is {\it 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 when parameterized by treewidth and maximum capacity of the vertices. This algorithm is further extended to obtain pseudo-polynomial time approximation schemes for planar graphs.

Affiliated with

Also associated with

No associations

Rating

Approximation Algorithms for the Capacitated Domination Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximation Algorithms for the Capacitated Domination Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximation Algorithms for the Capacitated Domination Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-623973