Approximation Algorithms for Partial Covering Problems

Extended Abstract
  • Rajiv Gandhi
  • Samir Khuller
  • Aravind Srinivasan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)


We study the generalization of covering problems to partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-set cover, if each element occurs in at most f sets, then we derive a primal-dual f-approximation algorithm (thus implying a 2-approximation for k-vertex cover) in polynomial time. In addition to its simplicity, this algorithm has the advantage of being parallelizable. For instances where each set has cardinality at most three, we obtain an approximation of 4/3. We also present better-than-2-approximation algorithms for k-vertex cover on bounded degree graphs, and for vertex cover on expanders of bounded average degree. We obtain a polynomial-time approximation scheme for k-vertex cover on planar graphs, and for covering points in R d by disks.

Keywords and Phrases

Approximation algorithms partial covering set cover vertex cover primal-dual methods randomized rounding 


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Copyright information

© Sprunger-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Rajiv Gandhi
    • 1
  • Samir Khuller
    • 2
  • Aravind Srinivasan
    • 3
  1. 1.Department of Computer ScienceUniversity of MarylandMD
  2. 2.Department of Computer Science and Institute for Advanced Computer StudiesUniversity of MarylandMD
  3. 3.Bell LabsLucent TechnologiesMurray Hill

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