Algorithmica

, Volume 65, Issue 3, pp 498–516 | Cite as

Improved Approximation Algorithms for the Spanning Star Forest Problem

  • Ning Chen
  • Roee Engelberg
  • C. Thach Nguyen
  • Prasad Raghavendra
  • Atri Rudra
  • Gyanit Singh
Article

Abstract

A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-disjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all vertices of G and has the maximum number of edges. This problem is the complement of the dominating set problem in the following sense: On a graph with n vertices, the size of the maximum spanning star forest is equal to n minus the size of the minimum dominating set.

We present a 0.71-approximation algorithm for this problem, improving upon the approximation factor of 0.6 of Nguyen et al. (SIAM J. Comput. 38:946–962, 2008). We also present a 0.64-approximation algorithm for the problem on node-weighted graphs. Finally, we present improved hardness of approximation results for the weighted (both edge-weighted and node-weighted) versions of the problem.

Our algorithms use a non-linear rounding scheme, which might be of independent interest.

Keywords

Approximation algorithms Spanning star forest problem 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ning Chen
    • 1
  • Roee Engelberg
    • 2
  • C. Thach Nguyen
    • 3
  • Prasad Raghavendra
    • 4
  • Atri Rudra
    • 5
  • Gyanit Singh
    • 3
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore
  2. 2.Department of Computer ScienceTechnionHaifaIsrael
  3. 3.Department of Computer Science & EngineeringUniversity of WashingtonSeattleUSA
  4. 4.School of Computer ScienceGeorgia Institute of TechnologyAtlantaUSA
  5. 5.Department of Computer Science & EngineeringUniversity at Buffalo, State University of New YorkBuffaloUSA

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