TY - JOUR

T1 - The k-path tree matroid and its applications to survivable network design

AU - Arkin, Esther M.

AU - Hassin, Refael

N1 - Funding Information:
We thank Klaus Truemper for the proof of Theorem 2.1 which simplifies our original proof. The first author was partially supported by the NSF grant CCF-0431030.

PY - 2008/5

Y1 - 2008/5

N2 - 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.

AB - 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.

KW - Algorithm

KW - Matroid intersection

KW - Network connectivity

UR - http://www.scopus.com/inward/record.url?scp=41149178231&partnerID=8YFLogxK

U2 - 10.1016/j.disopt.2006.11.009

DO - 10.1016/j.disopt.2006.11.009

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AN - SCOPUS:41149178231

SN - 1572-5286

VL - 5

SP - 314

EP - 322

JO - Discrete Optimization

JF - Discrete Optimization

IS - 2

ER -