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Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More

Author Mihail Stoian

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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • doubling constant parametrization
  • weighted problems
  • traveling salesman
  • weighted max-cut
  • edge-weighted k-clique

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Abstract

Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups. Currently, the only way to repurpose the algorithm of the unweighted version for the weighted version is to employ a polynomial embedding of the input weights. This, however, introduces a pseudo-polynomial factor into the running time, which becomes impractical for arbitrarily weighted instances.
In this paper, we introduce a new way to repurpose the algorithm of the unweighted problem. Specifically, we show that the time complexity of several well-known NP-hard problems operating over the (min, +) and (max, +) semirings, such as TSP, Weighted Max-Cut, and Edge-Weighted k-Clique, is proportional to that of their unweighted versions when the set of input weights has small doubling. We achieve this by a meta-algorithm that converts the input weights into polynomially bounded integers using the recent constructive Freiman’s theorem by Randolph and Węgrzycki [ESA 2024] before applying the polynomial embedding.

Cite As Get BibTex

Mihail Stoian. Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.79

Author Details

Mihail Stoian
  • University of Technology Nuremberg, Germany

Acknowledgements

The author thanks the anonymous reviewers of STACS'25 and STACS'26, whose detailed comments visibly improved the quality of the presentation.

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