Deterministic approximation for the volume of the truncated fractional matching polytope

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+δΔ], and δ≤CΔ 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+δΔ] as well, where δ≤CΔ−2k−3k−1k−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.