A note on the Survivable Network Design Problem

TL;DR

This paper presents a new counting argument for a known approximation algorithm for the survivable network design problem and explores connections between different problem variants, leading to improved approximation results.

Contribution

It introduces a novel counting technique for the iterated rounding approach and links hypergraphic SNDP to other variants, enabling a simpler 2-approximation for element connectivity SNDP.

Findings

A new counting argument improves the analysis of Jain's 2-approximation.

Connections between hypergraphic and edge/node-weighted SNDP variants are established.

A 2-approximation for element connectivity SNDP is achieved without set-pair relaxation.

Abstract

In this note we consider the survivable network design problem (SNDP) in undirected graphs. We make two contributions. The first is a new counting argument in the iterated rounding based 2-approximation for edge-connectivity SNDP (EC-SNDP) originally due to Jain. The second is to make some additional connections between hypergraphic version of SNDP introduced by Zhao, Nagamochi and Ibaraki and edge and node-weighted versions of EC-SNDP and element-connectivity SNDP (Elem-SNDP). One useful consequence of this connection is a 2-approximation for Elem-SNDP that avoids the use of set-pair based relaxation and analysis.