research-article

Deterministic, near-linear 𝜀-approximation algorithm for geometric bipartite matching

Authors:

Pankaj K. Agarwal,

Hsien-Chih Chang,

Sharath Raghvendra,

Allen XiaoAuthors Info & Claims

STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing

Pages 1052 - 1065

https://doi.org/10.1145/3519935.3519977

Published: 10 June 2022 Publication History

Abstract

Given two point sets A and B in ℝ^d of size n each, for some constant dimension d≥ 1, and a parameter ε>0, we present a deterministic algorithm that computes, in n·(ε⁻¹ logn)^O(d) time, a perfect matching between A and B whose cost is within a (1+ε) factor of the optimal matching under any ℓ_p-norm. Although a Monte-Carlo algorithm with a similar running time is proposed by Raghvendra and Agarwal [J. ACM 2020], the best-known deterministic ε-approximation algorithm takes Ω(n^3/2) time. Our algorithm constructs a (refinement of a) tree cover of ℝ^d, and we develop several new tools to apply a tree-cover based approach to compute an ε-approximate perfect matching.

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Cited By

Karim Abu-Affash ABhore SCarmi P(2024)Dynamic Euclidean Bottleneck MatchingTheoretical Computer Science10.1016/j.tcs.2024.114727(114727)Online publication date: Jul-2024
https://doi.org/10.1016/j.tcs.2024.114727
Fox ELu J(2023)A deterministic near-linear time approximation scheme for geometric transportation2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00078(1301-1315)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00078

Index Terms

Deterministic, near-linear 𝜀-approximation algorithm for geometric bipartite matching
1. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
  2. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing

June 2022

1698 pages

ISBN:9781450392648

DOI:10.1145/3519935

General Chair:
Stefano Leonardi
Sapienza University of Rome, Italy
,
Program Chair:
Anupam Gupta
Carnegie Mellon University, USA

Copyright © 2022 ACM.

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Published: 10 June 2022

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STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing

June 20 - 24, 2022

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Cited By

Karim Abu-Affash ABhore SCarmi P(2024)Dynamic Euclidean Bottleneck MatchingTheoretical Computer Science10.1016/j.tcs.2024.114727(114727)Online publication date: Jul-2024
https://doi.org/10.1016/j.tcs.2024.114727
Fox ELu J(2023)A deterministic near-linear time approximation scheme for geometric transportation2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00078(1301-1315)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00078

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