Optimization Letters

, Volume 4, Issue 3, pp 311–320 | Cite as

Approximation algorithms for finding and partitioning unit-disk graphs into co-k-plexes

  • Balabhaskar Balasundaram
  • Shyam Sundar Chandramouli
  • Svyatoslav Trukhanov
Original Paper

Abstract

This article studies a degree-bounded generalization of independent sets called co-k-plexes. Constant factor approximation algorithms are developed for the maximum co-k-plex problem on unit-disk graphs. The related problem of minimum co-k-plex coloring that generalizes classical vertex coloring is also studied in the context of unit-disk graphs. We extend several classical approximation results for independent sets in UDGs to co-k-plexes, and settle a recent conjecture on the approximability of co-k-plex coloring in UDGs.

Keywords

Unit-disk graph Independent set Graph coloring Co-k-plex k-dependent set Defective coloring t-improper coloring 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Balabhaskar Balasundaram
    • 1
  • Shyam Sundar Chandramouli
    • 2
  • Svyatoslav Trukhanov
    • 3
  1. 1.School of Industrial Engineering and ManagementOklahoma State UniversityStillwaterUSA
  2. 2.Indian Institute of Technology-MadrasChennaiIndia
  3. 3.Microsoft CorporationRedmondUSA

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