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Title:Maximum matchings in geometric intersection graphs
Authors:ID Bonnet, Édouard (Author)
ID Cabello, Sergio (Author)
ID Mulzer, Wolfgang (Author)
Files:.pdf PDF - Presentation file, download (576,69 KB)
MD5: CFA5DBABF17761B11ACC25F11DBAF784
 
URL URL - Source URL, visit https://link.springer.com/article/10.1007/s00454-023-00564-3
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:Let G be an intersection graph of n geometric objects in the plane. We show that a maximum matching in G can be found in O(ρ3ω/2nω/2) time with high probability, where ρ is the density of the geometric objects and ω>2 is a constant such that n×n matrices can be multiplied in O(nω) time. The same result holds for any subgraph of G, as long as a geometric representation is at hand. For this, we combine algebraic methods, namely computing the rank of a matrix via Gaussian elimination, with the fact that geometric intersection graphs have small separators. We also show that in many interesting cases, the maximum matching problem in a general geometric intersection graph can be reduced to the case of bounded density. In particular, a maximum matching in the intersection graph of any family of translates of a convex object in the plane can be found in O(nω/2) time with high probability, and a maximum matching in the intersection graph of a family of planar disks with radii in [1,Ψ] can be found in O(Ψ6log11n+Ψ12ωnω/2) time with high probability.
Keywords:computational geometry, geometric intersection graphs, disk graphs, unit-disk graphs, matchings
Publication status:Published
Publication version:Version of Record
Publication date:01.10.2023
Year of publishing:2023
Number of pages:str. 550-579
Numbering:Vol. 70, iss. 3
PID:20.500.12556/DiRROS-18632 New window
UDC:004.42:515.17
ISSN on article:0179-5376
DOI:10.1007/s00454-023-00564-3 New window
COBISS.SI-ID:163998979 New window
Note:
Publication date in DiRROS:08.04.2024
Views:596
Downloads:299
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BONNET, Édouard, CABELLO, Sergio and MULZER, Wolfgang, 2023, Maximum matchings in geometric intersection graphs. Discrete & computational geometry [online]. 2023. Vol. 70, no. 3, p. 550–579. [Accessed 7 April 2025]. DOI 10.1007/s00454-023-00564-3. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=18632
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Record is a part of a journal

Title:Discrete & computational geometry
Shortened title:Discrete comput. geom.
Publisher:Springer
ISSN:0179-5376
COBISS.SI-ID:25342208 New window

Document is financed by a project

Funder:ARRS - Slovenian Research Agency
Project number:P1-0297
Funder:ARRS - Slovenian Research Agency
Project number:J1-9109
Funder:ARRS - Slovenian Research Agency
Project number:J1-8130
Funder:ARRS - Slovenian Research Agency
Project number:J1-8155
Funder:ARRS - Slovenian Research Agency
Project number:J1-1693
Funder:ARRS - Slovenian Research Agency
Project number:J1-2452
Funder:ARRS - Slovenian Research Agency
Project number:N1-0218
Funder:EC - European Commission
Project number:StG 757609

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

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