Analyzing the optimal neighborhood: Algorithms for budgeted and partial connected dominating set problems

Samir Khuller, Manish Purohit, Kanthi K. Sarpatwar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

24 Scopus citations

Abstract

We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem (PCDS), we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum subset of vertices that induces a connected subgraph of G and dominates at least n' vertices. We obtain the first polynomial time algorithm with an O(ln δ) approximation factor for this problem, thereby significantly extending the results of Guha and Khuller (Algorithmica, Vol. 20(4), Pages 374-387, 1998) for the connected dominating set problem. We note that none of the methods developed earlier can be applied directly to solve this problem. In the budgeted connected dominating set problem (BCDS), there is a budget on the number of vertices we can select, and the goal is to dominate as many vertices as possible. We obtain a -1/13(1 - 1/e) approximation algorithm for this problem. Finally, we show that our techniques extend to a more general setting where the profit function associated with a subset of vertices is a "special" submodular function. This general-ization captures the connected dominating set problem with capacities and/or weighted profits as special cases. This implies a O(lnq) approximation (where q denotes the quota) and an O( 1) approximation algorithms for the partial and budgeted versions of these problems. While the algorithms are simple, the results make a surprising use of the greedy set cover framework in defining a useful profit function.

Original languageEnglish (US)
Title of host publicationProceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
PublisherAssociation for Computing Machinery
Pages1702-1713
Number of pages12
ISBN (Print)9781611973389
StatePublished - Jan 1 2014
Event25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States
Duration: Jan 5 2014Jan 7 2014

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
CountryUnited States
CityPortland, OR
Period1/5/141/7/14

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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