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Approximation Algorithms for Maximum Matchings in Geometric Intersection Graphs

Authors Sariel Har-Peled , Everett Yang

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Matchings
  • disk intersection graphs
  • approximation algorithms

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Abstract

We present a (1-ε)-approximation algorithms for maximum cardinality matchings in disk intersection graphs - all with near linear running time. We also present an estimation algorithm that returns (1±ε)-approximation to the size of such matchings - this algorithm runs in linear time for unit disks, and O(n log n) for general disks (as long as the density is relatively small).

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Sariel Har-Peled and Everett Yang. Approximation Algorithms for Maximum Matchings in Geometric Intersection Graphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 47:1-47:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SoCG.2022.47

Author Details

Sariel Har-Peled
  • Department of Computer Science, University of Illinois, 201 N. Goodwin Avenue, Urbana, IL 61801, USA
Everett Yang
  • Department of Computer Science, University of Illinois, 201 N. Goodwin Avenue, Urbana, IL 61801, USA

Funding

  • Har-Peled, Sariel: Work on this paper was partially supported by a NSF AF award CCF-1907400.

Acknowledgements

The authors thank the anonymous referees for their detailed comments.

References

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