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Engineering Weighted Connectivity Augmentation Algorithms

Authors Marcelo Fonseca Faraj , Ernestine Großmann , Felix Joos , Thomas Möller , Christian Schulz

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Author Details

Marcelo Fonseca Faraj
  • Heidelberg University, Heidelberg, Germany
Ernestine Großmann
  • Heidelberg University, Heidelberg, Germany
Felix Joos
  • Heidelberg University, Heidelberg, Germany
Thomas Möller
  • Heidelberg University, Heidelberg, Germany
Christian Schulz
  • Heidelberg University, Heidelberg, Germany

Funding

We acknowledge support by DFG grant SCHU 2567/3-1.

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Marcelo Fonseca Faraj, Ernestine Großmann, Felix Joos, Thomas Möller, and Christian Schulz. Engineering Weighted Connectivity Augmentation Algorithms. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SEA.2024.11

Abstract

Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find a minimum cost subset of a given set of weighted links that increases the connectivity of a graph by one when the links are added to the edge set of the input instance. In this work, we give a first implementation of recently discovered better-than-2 approximations. Furthermore, we propose three new heuristics and one exact approach. These include a greedy algorithm considering link costs and the number of unique cuts covered, an approach based on minimum spanning trees and a local search algorithm that may improve a given solution by swapping links of paths. Our exact approach uses an ILP formulation with efficient cut enumeration as well as a fast initialization routine. We then perform an extensive experimental evaluation which shows that our algorithms are faster and yield the best solutions compared to the current state-of-the-art as well as the recently discovered better-than-2 approximation algorithms. Our novel local search algorithm can improve solution quality even further.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Optimization with randomized search heuristics
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Randomized local search
Keywords
  • weighted connectivity augmentation
  • approximation
  • heuristic
  • integer linear program
  • algorithm engineering

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