CIAC 1997: Algorithms and Complexity pp 13-24 | Cite as

Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5

  • Yefim Dinitz
  • Zeev Nutov
Regular Presentations
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1203)

Abstract

The problem of finding a minimum weight k-vertex connected spanning subgraph is considered. For k>1, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there are k internally vertex-disjoint paths to every other vertex), we derive polynomial time approximation algorithms for several values of k.
  1. (i)

    For k=3, we give an algorithm with approximation factor 2. This improves the best previously known factor 3.

     
  2. (ii)

    For k=4 and k=5, we give an algorithm with approximation factor 3. This improves the best previously known factors 4 1/6 and 4 17/30, respectively.

     

Keywords

Approximation Algorithm Minimum Weight Disjoint Path Span Subgraph Minimum Cost Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Yefim Dinitz
    • 1
  • Zeev Nutov
    • 2
  1. 1.Dept. of Computer ScienceTechnionHaifaIsrael
  2. 2.Dept. of MathematicsTechnionHaifaIsrael

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