The k-path tree matroid and its applications to survivable network design

We define the k-path tree matroid, and use it to solve network design problems in which the required connectivity is arbitrary for a given pair of nodes, and 1 for the other pairs. We solve the problems for undirected and directed graphs. We then use these exact algorithms to give improved approximation algorithms for problems in which the weights satisfy the triangle inequality and the connectivity requirement is either 2 among at most five nodes and 1 for the other nodes, or it is 3 among a set of three nodes and 1 for all other nodes. Mathematics subject classification: Discrete mathematics 68R99, connectivity 05C40.

• Type: Journal
• Year: 2008
• Where: DISOPT
• Authors: Esther M. Arkin, Refael Hassin
• Keywords: DISOPT 2008, K-path Tree, Network Design Problems, Required Connectivity