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

arXiv: https://arxiv.org/abs/1508.05567 · HTML: https://mlsanity.com/paper/1508.05567/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2015.

## Built on by (most cited first, 1 of 1)

- [Some Primal-Dual Theory for Subgradient Methods for Strongly Convex Optimization](https://mlsanity.com/paper/2305.17323/) (2023)

## Abstract (arXiv)

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≈ 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.