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arXiv · 2409.07283

Deterministic approximation for the volume of the truncated fractional matching polytope

Heng Guo·Vishvajeet N
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Abstract

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.

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Heng Guo, Vishvajeet N. 2024-09-11. Deterministic approximation for the volume of the truncated fractional matching polytope. https://arxiv.org/abs/2409.07283

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