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

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 11, 2, 5], but very little is known about the vertex version. In our problem, vertices are partitioned into two sets: terminals and non-terminals. Only edges and non-terminals 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 + 1 2 + + 1 n . Besides providing possible insights for solving the vertexdisjoint paths version, the element connectivity problem is of independent interest, since it models a realistic situation.

• Type: Journal
• Year: 2002
• Where: JAL
• Authors: Kamal Jain, Ion I. Mandoiu, Vijay V. Vazirani, David P. Williamson
• Keywords: Element Connectivity Problem, JAL 2002, Survivable Network Design, Vertex-disjoint Paths