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Abstract
A matching is compatible to two or more labeled point sets of size n with labels { 1, ⋯, n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n 1 / ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n 2 / ( ℓ + 1 )) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.
Original language | English |
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Title of host publication | WALCOM |
Subtitle of host publication | Algorithms and Computation - 15th International Conference and Workshops, WALCOM 2021, Proceedings |
Editors | Ryuhei Uehara, Seok-Hee Hong, Subhas C. Nandy |
Pages | 221-233 |
Number of pages | 13 |
DOIs | |
Publication status | Published - 2021 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12635 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Keywords
- Compatible graphs
- Crossing-free matchings
- Geometric graphs
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science
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Dive into the research topics of 'On Compatible Matchings'. Together they form a unique fingerprint.Activities
- 1 Talk at conference or symposium
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On Compatible Matchings
Daniel Perz (Speaker)
2021Activity: Talk or presentation › Talk at conference or symposium › Science to science
Prizes
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Best Paper Award WALCOM 2021
Perz, Daniel (Recipient), Aichholzer, Oswin (Recipient), Vogtenhuber, Birgit (Recipient), De Parada, Irene Maria (Recipient), Arroyo, Alan (Recipient), Masárová, Zuzana (Recipient), Tkadlec, Josef (Recipient) & Pilz, Alexander (Recipient), 2021
Prize: Prizes / Medals / Awards