Bottleneck matching in the plane

Matthew J. Katz; Micha Sharir

doi:10.1016/j.comgeo.2023.101986

Bottleneck matching in the plane

Matthew J. Katz, Micha Sharir

Ben-Gurion University of the Negev, Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We present a randomized algorithm that with high probability finds a bottleneck matching in a set of n=2ℓ points in the plane. The algorithm's running time is O(n^ω/2log⁡n), where ω>2 is a constant such that any two n×n matrices can be multiplied in time O(n^ω). The state of the art in fast matrix multiplication allows us to set ω=2.3728596.

Original language	American English
Article number	101986
Journal	Computational Geometry: Theory and Applications
Volume	112
DOIs	https://doi.org/10.1016/j.comgeo.2023.101986
State	Published - 1 Jun 2023

Keywords

Bottleneck matching
Geometric optimization
Matrix multiplication
Order-k Voronoi diagram
Unit disk graph

All Science Journal Classification (ASJC) codes

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.comgeo.2023.101986

Cite this

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title = "Bottleneck matching in the plane",

abstract = "We present a randomized algorithm that with high probability finds a bottleneck matching in a set of n=2ℓ points in the plane. The algorithm's running time is O(nω/2log⁡n), where ω>2 is a constant such that any two n×n matrices can be multiplied in time O(nω). The state of the art in fast matrix multiplication allows us to set ω=2.3728596.",

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AB - We present a randomized algorithm that with high probability finds a bottleneck matching in a set of n=2ℓ points in the plane. The algorithm's running time is O(nω/2log⁡n), where ω>2 is a constant such that any two n×n matrices can be multiplied in time O(nω). The state of the art in fast matrix multiplication allows us to set ω=2.3728596.

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KW - Matrix multiplication

KW - Order-k Voronoi diagram

KW - Unit disk graph

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Bottleneck matching in the plane

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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