By Topic

An iterative rounding 2-approximation algorithm for the element connectivity problem

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
L. Fleischer ; Carnegie Mellon Univ., Pittsburgh, PA, USA ; K. Jain ; D. P. Williamson

In the survivable network design problem (SNDP), given an undirected graph and values rij for each pair of vertices i and j, we attempt to find a minimum-cost subgraph such that there are rij disjoint paths between vertices i and j. In the edge connected version of this problem (EC-SNDP), these paths must be edge-disjoint. In the vertex connected version of the problem (VC-SNDP), the paths must be vertex disjoint. K. Jain et al. (1999) propose a version of the problem intermediate in difficulty to these two, called the element connectivity problem (ELC-SNDP, or ELC). These variants of SNDP are all known to be NP-hard. The best known approximation algorithm for the EC-SNDP has performance guarantee of 2 (K. Jain, 2001), and iteratively rounds solutions to a linear programming relaxation of the problem. ELC has a primal-dual O (log k) approximation algorithm, where k=maxi,j rij. VC-SNDP is not known to have a non-trivial approximation algorithm; however, recently L. Fleischer (2001) has shown how to extend the technique of K. Jain ( 2001) to give a 2-approximation algorithm in the case that rij∈{0, 1, 2}. She also shows that the same techniques will not work for VC-SNDP for more general values of rij. The authors show that these techniques can be extended to a 2-approximation algorithm for ELC. This gives the first constant approximation algorithm for a general survivable network design problem which allows node failures.

Published in:

Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on

Date of Conference:

8-11 Oct. 2001