A primal-dual schema based approximation algorithm for the element connectivity problem

Authors:
Kamal Jain;Ion Mandoiu;Vijay V. Vazirani;David P. Williamson
Affiliations:
Microsoft Research, One Microsoft Way, Redmond, WA;University of California at San Diego, Computer Science and Engineering Department, La Jolla, CA;Georgia Institute of Technology, College of Computing, 801 Atlantic Drive, Atlanta, GA;IBM Almaden Research Center, 650 Harry Rd., San Jose, CA
Venue:
Journal of Algorithms
Year:
2002

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Abstract

The element connectivity problem falls in the category of survivable network design problems-it is intermediate to the versions that ask for edge-disjoint and vertex-disjoint paths. The edge version is by now well understood from the view-point of approximation algorithms [Williamson et al., Combinatorica 15 (1995) 435-454; Goemans et al., in: SODA '94, 223-232; Jain, Combinatorica 21 (2001) 39-60], but very little is known about the vertex version. In our problem, vertices are partitioned into two sets: terminals and nonterminals. Only edges and nonterminals can fail--we refer to them as elements--and only pairs of terminals have connectivity requirements, specifying the number of element-disjoint paths required. Our algorithm achieves an approximation guarantee of factor 2Hk, where k is the largest requirement and Hn = 1 + ½ +... + 1/n. Besides providing possible insights for solving the vertex-disjoint paths version, the element connectivity problem is of independent interest, since it models a realistic situation.