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Deterministic Approximation for the Volume of the Truncated Fractional Matching Polytope

Authors Heng Guo , Vishvajeet N

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Author Details

Heng Guo
  • School of Informatics, University of Edinburgh, UK
Vishvajeet N
  • School of Informatics, University of Edinburgh, UK

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 947778).

Cite As Get BibTex

Heng Guo and Vishvajeet N. Deterministic Approximation for the Volume of the Truncated Fractional Matching Polytope. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 57:1-57:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.57

Abstract

We give a deterministic polynomial-time approximation scheme (FPTAS) for the volume of the truncated fractional matching polytope for graphs of maximum degree Δ, where the truncation is by restricting each variable to the interval [0,(1+δ)/Δ], and δ ≤ C/Δ for some constant C > 0. We also generalise our result to the fractional matching polytope for hypergraphs of maximum degree Δ and maximum hyperedge size k, truncated by [0,(1+δ)/Δ] as well, where δ ≤ CΔ^{-(2k-3)/(k-1)}k^{-1} for some constant C > 0. The latter result generalises both the first result for graphs (when k = 2), and a result by Bencs and Regts (2024) for the truncated independence polytope (when Δ = 2). Our approach is based on the cluster expansion technique.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Theory of computation → Computational geometry
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • deterministic volume computation
  • cluster expansion
  • explicit polytopes

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