Fixed-parameter algorithms for minimum cost edge-connectivity augmentation

TL;DR

This paper studies fixed-parameter algorithms for minimum cost edge- and node-connectivity augmentation problems, showing fixed-parameter tractability and polynomial kernels for various connectivity increases.

Contribution

It introduces fixed-parameter algorithms and polynomial kernels for minimum cost edge- and node-connectivity augmentation problems, advancing the understanding of their computational complexity.

Findings

Fixed-parameter tractability for augmenting from k-1 to k connectivity with p edges.

Polynomial kernels for the augmentation problems.

FPT results for increasing edge- and node-connectivity from 0 to 2 and 1 to 2.

Abstract

We consider connectivity-augmentation problems in a setting where each potential new edge has a nonnegative cost associated with it, and the task is to achieve a certain connectivity target with at most p new edges of minimum total cost. The main result is that the minimum cost augmentation of edge-connectivity from k-1 to k with at most p new edges is fixed-parameter tractable parameterized by p and admits a polynomial kernel. We also prove the fixed-parameter tractability of increasing edge-connectivity from 0 to 2, and increasing node-connectivity from 1 to 2.