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

TL;DR

This paper introduces a dual-based approximation approach for various NP-Complete network connectivity problems, achieving improved ratios and new bounds for problems like DPA, MSCS, and SSC.

Contribution

The paper presents a novel dual-based method for cut-based LP relaxations, providing improved approximation algorithms for several network design problems.

Findings

Achieves a 3/2-approximation for Minimum 2-Edge-Connected Spanning Subgraph.

Improves the approximation ratio for Dual Power Assignment to 3/2.

Provides a 1.6-approximation for Star Strong Connectivity and new bounds on integrality gaps.

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 $11/7\approx 1.57$. 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.