2026-07-21T03:18:02Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26072 2026-06-23T13:18:57Z ddc:004 open_access

Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates Park, Seongbin Oh, Eunjin Edge cover many-to-many matching similarity geometric matching 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Seongbin Park and Eunjin Oh 2026 Is Part Of LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2026.36 urn:nbn:de:0030-drops-260728 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.36 eng https://creativecommons.org/licenses/by/4.0/legalcode