Parameterized approximation algorithms for some location problems in graphs

Document Type

Article

Department or Administrative Unit

Computer Science

Publication Date

1-10-2019

Abstract

We develop efficient parameterized, with additive error, approximation algorithms for the (Connected) r-Domination problem and the (Connected) p-Center problem for unweighted and undirected graphs. Given a graphG, we show how to construct a (connected) (r+O(μ))-dominating set D with |D| ≤|D∗|efficiently. Here, D∗ is a minimum (connected) r-dominating set of G and μ is our graph parameter, which is the tree-breadth or the cluster diameter in a layering partition of G. Additionally, we show that a +O(μ)-approximation for the (Connected) p-Center problem on G can be computed in polynomial time. Our interest in these parameters stems from the fact that in many real-world networks, including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others, and in many structured classes of graphs these parameters are small constants.

Comments

This article was originally published in Theoretical Computer Science. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

An author-supplied version of this text is hosted by the arXiv repository.

Journal

Theoretical Computer Science

Rights

© 2018 Elsevier B.V. All rights reserved.

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