Packing Plane Perfect Matchings into a Point Set
Ahmad Biniaz, Prosenjit Bose, Anil Maheshwari, Michiel Smid

TL;DR
This paper investigates the maximum number of plane perfect matchings that can be packed into a set of points in the plane, providing lower bounds and exact counts for special configurations.
Contribution
It establishes a logarithmic lower bound on the number of plane perfect matchings that can be packed into any point set and determines exact counts for certain special cases.
Findings
At least loor(log_2 n) plane perfect matchings can be packed into any point set.
Exact number of matchings is determined for some special point configurations.
Extensions of the problem are also discussed.
Abstract
Given a set of points in the plane, where is even, we consider the following question: How many plane perfect matchings can be packed into ? We prove that at least plane perfect matchings can be packed into any point set . For some special configurations of point sets, we give the exact answer. We also consider some extensions of this problem.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Optimization and Packing Problems · 3D Shape Modeling and Analysis
