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arXiv · 2407.04989

FPTAS for Holant Problems with Log-Concave Signatures

Kun He·Zhidan Li·Guoliang Qiu·Chihao Zhang
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Abstract

For an integer $b\ge 0$, a $b$-matching in a graph $G=(V,E)$ is a set $S\subseteq E$ such that each vertex $v\in V$ is incident to at most $b$ edges in $S$. We design a fully polynomial-time approximation scheme (FPTAS) for counting the number of $b$-matchings in graphs with bounded degrees. Our FPTAS also applies to a broader family of counting problems, namely Holant problems with log-concave signatures. Our algorithm is based on Moitra's linear programming approach (JACM'19). Using a novel construction called the extended coupling tree, we derandomize the coupling designed by Chen and Gu (SODA'24).

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Kun He, Zhidan Li, Guoliang Qiu, Chihao Zhang. 2024-07-06. FPTAS for Holant Problems with Log-Concave Signatures. https://arxiv.org/abs/2407.04989

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