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

Authors Seongbin Park , Eunjin Oh

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LIPIcs.SWAT.2026.36.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Computational geometry
Keywords
  • Edge cover
  • many-to-many matching
  • similarity
  • geometric matching

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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 ⊂ [Δ]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 Õ(n²) time. We present an exact Õ(n^{1.5} log Δ) time algorithm for point sets in [Δ]². To the best of our knowledge, this is the first subquadratic exact algorithm for planar many-to-many matching under bounded integer coordinates.

Cite As Get BibTex

Seongbin Park and Eunjin Oh. Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.36

Author Details

Seongbin Park
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Eunjin Oh
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea

Funding

Supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. RS-2024-00440239, Sublinear Scalable Algorithms for Large-Scale Data Analysis) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2024-00358505).

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