An Improved Approximation Algorithm for Minimum-Cost Subset k-Connectivity

(Extended Abstract)
  • Bundit Laekhanukit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

The minimum-cost subset k-connected subgraph problem is a cornerstone problem in the area of network design with vertex connectivity requirements. In this problem, we are given a graph G = (V,E) with costs on edges and a set of terminals T. The goal is to find a minimum cost subgraph such that every pair of terminals are connected by k openly (vertex) disjoint paths. In this paper, we present an approximation algorithm for the subset k-connected subgraph problem which improves on the previous best approximation guarantee of O(k 2logk) by Nutov (FOCS 2009). Our approximation guarantee, α(|T |), depends upon the number of terminals:
$$ \alpha(|T|) \ \ =\ \ \begin{cases} O(|T|^2) &\mbox{if } |T| < 2k\\ O(k \log^2 k) & \mbox{if } 2k\le |T| < k^2\\ O(k \log k) & \mbox{if } |T| \ge k^2 \end{cases} $$
So, when the number of terminals is large enough, the approximation guarantee improves significantly. Moreover, we show that, given an approximation algorithm for |T | = k, we can obtain almost the same approximation guarantee for any instances with |T | > k. This suggests that the hardest instances of the problem are when |T | ≈ k.

Keywords

Approximation Algorithm Network Design Outer Iteration Disjoint Path Network Design Problem 
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 2011

Authors and Affiliations

  • Bundit Laekhanukit
    • 1
  1. 1.School of Computer ScienceMcGill UniversityCanada

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