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

Authors:
Esther M. Arkin;Refael Hassin
Affiliations:
Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY 11794-3600, United States;School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
Venue:
Discrete Optimization
Year:
2008

Citing 13
Cited 0

A matroid algorithm and its application to the efficient solution of two optimization problems on graphs

Mathematical Programming: Series A and B
Algorithms and data structures for an expanded family of matroid intersection problems

SIAM Journal on Computing
The point-to-point delivery and connection problems: complexity and algorithms

Discrete Applied Mathematics
Network flows: theory, algorithms, and applications

Network flows: theory, algorithms, and applications
On the point-to-point connection problem

Information Processing Letters
The point-to-point connection problem—analysis and algorithms

Discrete Applied Mathematics
Designing Hierarchical Survivable Networks

Operations Research
The Directed Steiner Network Problem is Tractable for a Constant Number of Terminals

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Connectivity–splitting models for survivable network design

Networks
Algorithms for a network design problem with crossing supermodular demands

Networks
Design of Survivable Networks: A survey

Networks
A note on relatives to the Held and Karp 1-tree problem

Operations Research Letters
Intuitive solution-doubling techniques for worst-case analysis of some survivable network design problems

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.