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.
@InProceedings{guo_et_al:LIPIcs.ITCS.2025.57, author = {Guo, Heng and N, Vishvajeet}, title = {{Deterministic Approximation for the Volume of the Truncated Fractional Matching Polytope}}, booktitle = {16th Innovations in Theoretical Computer Science Conference (ITCS 2025)}, pages = {57:1--57:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-361-4}, ISSN = {1868-8969}, year = {2025}, volume = {325}, editor = {Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.57}, URN = {urn:nbn:de:0030-drops-226858}, doi = {10.4230/LIPIcs.ITCS.2025.57}, annote = {Keywords: deterministic volume computation, cluster expansion, explicit polytopes} }
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