Deterministic approximation for the volume of the truncated fractional matching polytope
<|reference_start|>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 $\Delta$, where the truncation is by restricting each variable to the interval $[0,\frac{1+\delta}{\Delta}]$, and $\delta\le \frac{C}{\Delta}$ for some constant $C>0$. We also generalise our result to the fractional matching polytope for hypergraphs of maximum degree $\Delta$ and maximum hyperedge size $k$, truncated by $[0,\frac{1+\delta}{\Delta}]$ as well, where $\delta\le C\Delta^{-\frac{2k-3}{k-1}}k^{-1}$ 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 $\Delta=2$). Our approach is based on the cluster expansion technique.<|reference_end|>
@article{guo2024deterministic,
    title={Deterministic approximation for the volume of the truncated fractional
  matching polytope},
    author={Heng Guo, Vishvajeet N},
    journal={arXiv preprint arXiv:2409.07283},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.07283},
    primaryClass={cs.DS cs.DM math.CO}
}