A Deterministic Algorithm for the Vertex Connectivity Survivable Network Design Problem

TL;DR

This paper presents deterministic algorithms for the vertex connectivity survivable network design problem, improving upon previous randomized solutions by providing explicit, reliable methods with proven approximation guarantees.

Contribution

It derandomizes existing algorithms for the general problem and introduces a new deterministic algorithm for the single-source variant, both with competitive approximation factors.

Findings

Deterministic O(k^3 log n) algorithm for the general problem

Deterministic O(k^2 log n) algorithm for the single-source problem

Improved reliability over randomized algorithms

Abstract

In the vertex connectivity survivable network design problem we are given an undirected graph G = (V,E) and connectivity requirement r(u,v) for each pair of vertices u,v. We are also given a cost function on the set of edges. Our goal is to find the minimum cost subset of edges such that for every pair (u,v) of vertices we have r(u,v) vertex disjoint paths in the graph induced by the chosen edges. Recently, Chuzhoy and Khanna presented a randomized algorithm that achieves a factor of O(k^3 log n) for this problem where k is the maximum connectivity requirement. In this paper we derandomize their algorithm to get a deterministic O(k^3 log n) factor algorithm. Another problem of interest is the single source version of the problem, where there is a special vertex s and all non-zero connectivity requirements must involve s. We also give a deterministic O(k^2 log n) algorithm for this problem.