# A near-linear time ε-approximation algorithm for geometric bipartite matching

Published

Journal Article

For point sets A,B ⊂ ℝ d, |A|=|B|=n, and for a parameter ε > 0, we present an algorithm that computes, in O(n poly(log n, 1/ε)) time, an ε-approximate perfect matching of A and B with high probability; the previously best known algorithm takes Ω(n 3/2) time. We approximate the L p-norm using a distance function, d(·,·) based on a randomly shifted quad-tree. The algorithm iteratively generates an approximate minimum-cost augmenting path under d(·,·) in time proportional to the length of the path. We show that the total length of the augmenting paths generated by the algorithm is O((n/ε)log n), implying that the running time of our algorithm is O(n poly(log n,1/ε)). © 2012 ACM.

### Full Text

### Duke Authors

### Cited Authors

- Sharathkumar, R; Agarwal, PK

### Published Date

- June 26, 2012

### Published In

### Start / End Page

- 385 - 394

### International Standard Serial Number (ISSN)

- 0737-8017

### Digital Object Identifier (DOI)

- 10.1145/2213977.2214014

### Citation Source

- Scopus