Approximating Flexible Graph Connectivity via R\"acke Tree based Rounding

TL;DR

This paper advances the understanding of flexible graph connectivity by adapting R"acke tree-based rounding techniques to achieve poly-logarithmic approximations for fixed-connectivity survivable network design problems.

Contribution

It introduces a novel application of R"acke trees and group Steiner tree rounding to approximate flexible graph connectivity, providing new bounds and insights.

Findings

Achieves poly-logarithmic approximation for fixed-connectivity Flex-SNDP.

Establishes an upper bound on the LP relaxation integrality gap.

Adapts recent survivable network design frameworks to flexible connectivity.

Abstract

Flexible graph connectivity is a new network design model introduced by Adjiashvili. It has seen several recent algorithmic advances. Despite these, the approximability even in the setting of a single-pair $(s,t)$ is poorly understood. In our recent work, we raised the question of whether there is poly-logarithmic approximation for the survivable network design version (Flex-SNDP) when the connectivity requirements are fixed constants. In this paper, we adapt a powerful framework for survivable network design recently developed by Chen, Laekhanukit, Liao, and Zhang to give an affirmative answer to the question. The framework of is based on R\"acke trees and group Steiner tree rounding. The algorithm and analysis also establishes an upper bound on the integrality gap of an LP relaxation for Flex-SNDP.