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Dual Charging for Half-Integral TSP

Authors Nathan Klein , Mehrshad Taziki

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ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Approximation Algorithms
  • Graph Algorithms
  • Randomized Rounding
  • Linear Programming

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Abstract

In this extended abstract, we show that the max entropy algorithm is a randomized 1.49776 approximation for half-integral TSP, improving upon the previous known bound of 1.49993 from Karlin et al. This also improves upon the best-known approximation for half-integral TSP due to Gupta et al. Our improvement results from using the dual, instead of the primal, to analyze the expected cost of the matching. We believe this method of analysis could lead to a simpler proof that max entropy is a better-than-3/2 approximation in the general case.

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Nathan Klein and Mehrshad Taziki. Dual Charging for Half-Integral TSP. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.21

Author Details

Nathan Klein
  • Department of Computer Science, Boston University, MA, USA
Mehrshad Taziki
  • Department of Computer Science, ETH Zürich, Zürich, Switzerland

References

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