Approximation Algorithms for Connected Graph Factors of Minimum Weight

Approximation Algorithms for Connected Graph Factors of Minimum Weight Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning subgraphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ratios for all d≥2⋅⌈k/2⌉. For the case of k-vertex-connectedness, we achieve constant approximation ratios for d≥2k−1. Our algorithms also work for arbitrary degree sequences if the minimum degree is at least 2⋅⌈k/2⌉ (for k-edge-connectivity) or 2k−1 (for k-vertex-connectivity). To complement our approximation algorithms, we prove that the problem with simple connectivity cannot be approximated better than the traveling salesman problem. In particular, the problem is A P X-hard. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory of Computing Systems Springer Journals

Approximation Algorithms for Connected Graph Factors of Minimum Weight

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Publisher
Springer US
Copyright
Copyright © 2016 by The Author(s)
Subject
Computer Science; Theory of Computation
ISSN
1432-4350
eISSN
1433-0490
D.O.I.
10.1007/s00224-016-9723-z
Publisher site
See Article on Publisher Site

Abstract

Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning subgraphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ratios for all d≥2⋅⌈k/2⌉. For the case of k-vertex-connectedness, we achieve constant approximation ratios for d≥2k−1. Our algorithms also work for arbitrary degree sequences if the minimum degree is at least 2⋅⌈k/2⌉ (for k-edge-connectivity) or 2k−1 (for k-vertex-connectivity). To complement our approximation algorithms, we prove that the problem with simple connectivity cannot be approximated better than the traveling salesman problem. In particular, the problem is A P X-hard.

Journal

Theory of Computing SystemsSpringer Journals

Published: Nov 16, 2016

References

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