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arXiv · 2102.12646

Spanning Tree Constrained Determinantal Point Processes are Hard to (Approximately) Evaluate

Tatsuya Matsuoka·Naoto Ohsaka
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Abstract

We consider determinantal point processes (DPPs) constrained by spanning trees. Given a graph $G=(V,E)$ and a positive semi-definite matrix $\mathbf{A}$ indexed by $E$, a spanning-tree DPP defines a distribution such that we draw $S\subseteq E$ with probability proportional to $\det(\mathbf{A}_S)$ only if $S$ induces a spanning tree. We prove $\sharp\textsf{P}$-hardness of computing the normalizing constant for spanning-tree DPPs and provide an approximation-preserving reduction from the mixed discriminant, for which FPRAS is not known. We show similar results for DPPs constrained by forests.

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Tatsuya Matsuoka, Naoto Ohsaka. 2021-02-25. Spanning Tree Constrained Determinantal Point Processes are Hard to (Approximately) Evaluate. https://doi.org/10.1016/j.orl.2021.02.004

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