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An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem

Authors Luke Hawranick, Matthew Williamson , Jacob Restanio , K. Subramani , Cody Klingler

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Subject Classification

ACM Subject Classification
  • Networks → Network algorithms
  • Theory of computation → Approximation algorithms analysis
  • General and reference → Empirical studies
Keywords
  • Graphs
  • Networks
  • Tree Augmentation
  • Approximation Algorithms
  • Empirical

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Abstract

In this paper, we perform an experimental study of approximation algorithms for the unweighted tree augmentation problem (UTAP). Our goal is to establish a baseline performance for several existing approximation algorithms on actual instances rather than worst-case instances. In particular, we are interested in whether the algorithms' performance in practical instances is consistent with their worst-case guarantee rankings. We are also interested in whether preprocessing times, implementation difficulties, and running times justify the use of an algorithm in practice. We profile and analyze three approximation algorithms from the literature against a simple randomized algorithm. The performance of each algorithm was evaluated using metrics for space usage, running time, and solution quality. We found that the simple randomized algorithm is very competitive with the approximation algorithms and that the algorithms do not necessarily rank according to their theoretical guarantees. The randomized algorithm is easier to implement and understand, using less space than any of the more sophisticated approximation algorithms.

Cite As Get BibTex

Luke Hawranick, Matthew Williamson, Jacob Restanio, K. Subramani, and Cody Klingler. An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SEA.2026.21

Author Details

Luke Hawranick
  • University of South Carolina, Columbia, SC, USA
Matthew Williamson
  • Marietta College, OH, USA
Jacob Restanio
  • West Virginia University, Morgantown, WV, USA
K. Subramani
  • West Virginia University, Morgantown, WV, USA
Cody Klingler
  • West Virginia University, Morgantown, WV, USA

Funding

  • Subramani, K.: Supported in part by the National Science Foundation through grant CCF-2525738 and the Defense Advanced Research Projects Agency through grant HR0011-25-2-0027.

Supplementary Materials

References

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