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Dual-Based Approximation Algorithms for Cut-Based Network Connectivity Problems

Dual-Based Approximation Algorithms for Cut-Based Network Connectivity Problems We consider a variety of NP-Complete network connectivity problems. We introduce a novel dual-based approach to approximating network design problems with cut-based linear programming relaxations. This approach gives a 3/2-approximation to Minimum 2-Edge-Connected Spanning Subgraph that is equivalent to a previously proposed algorithm. One well-studied branch of network design models ad hoc networks where each node can either operate at high or low power. If we allow unidirectional links, we can formalize this into the problem Dual Power Assignment (DPA). Our dual-based approach gives a 3 / 2-approximation to DPA, improving the previous best approximation known of $$11/7\approx 1.57$$ 11 / 7 ≈ 1.57 . Another standard network design problem is Minimum Strongly Connected Spanning Subgraph (MSCS). We propose a new problem generalizing MSCS and DPA called Star Strong Connectivity (SSC). Then we show that our dual-based approach achieves a 1.6-approximation ratio on SSC. As a consequence of our dual-based approximations, we prove new upper bounds on the integrality gaps of these problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

Dual-Based Approximation Algorithms for Cut-Based Network Connectivity Problems

Grimmer, Benjamin
Algorithmica , Volume 80 (10) – Aug 7, 2017
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25 pages

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
DOI
10.1007/s00453-017-0356-7
Publisher site
See Article on Publisher Site

Abstract

We consider a variety of NP-Complete network connectivity problems. We introduce a novel dual-based approach to approximating network design problems with cut-based linear programming relaxations. This approach gives a 3/2-approximation to Minimum 2-Edge-Connected Spanning Subgraph that is equivalent to a previously proposed algorithm. One well-studied branch of network design models ad hoc networks where each node can either operate at high or low power. If we allow unidirectional links, we can formalize this into the problem Dual Power Assignment (DPA). Our dual-based approach gives a 3 / 2-approximation to DPA, improving the previous best approximation known of $$11/7\approx 1.57$$ 11 / 7 ≈ 1.57 . Another standard network design problem is Minimum Strongly Connected Spanning Subgraph (MSCS). We propose a new problem generalizing MSCS and DPA called Star Strong Connectivity (SSC). Then we show that our dual-based approach achieves a 1.6-approximation ratio on SSC. As a consequence of our dual-based approximations, we prove new upper bounds on the integrality gaps of these problems.

Journal

Algorithmica – Springer Journals

Published: Aug 7, 2017

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