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arXiv · 2604.16921

Exact Subquadratic Algorithm for Many-to-Many Matching on Planar Point Sets with Integer Coordinates

Seongbin Park·Eunjin Oh
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Abstract

In this paper, we study the many-to-many matching problem on planar point sets with integer coordinates: Given two disjoint sets $R,B \subset [\Delta]^2$ with $|R|+|B|=n$, the goal is to select a set of edges between $R$ and $B$ so that every point is incident to at least one edge and the total Euclidean length is minimized. In the general case that $R$ and $B$ are point sets in the plane, the best-known algorithm for the many-to-many matching problem takes $\tilde{O}(n^2)$ time. We present an exact $\tilde{O}(n^{1.5} \log \Delta)$ time algorithm for point sets in $[\Delta]^2$. To the best of our knowledge, this is the first subquadratic exact algorithm for planar many-to-many matching under bounded integer coordinates.

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Seongbin Park, Eunjin Oh. 2026-04-18. Exact Subquadratic Algorithm for Many-to-Many Matching on Planar Point Sets with Integer Coordinates. https://arxiv.org/abs/2604.16921

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