Efficient algorithms for geometric partial matching

Published

Conference Paper

© Pankaj K. Agarwal, Hsien-Chih Chang, and Allen Xiao. Let A and B be two point sets in the plane of sizes r and n respectively (assume r ≤ n), and let k be a parameter. A matching between A and B is a family of pairs in A × B so that any point of A ∪ B appears in at most one pair. Given two positive integers p and q, we define the cost of matching M to be c(M) = Σ (a,b)ϵ M ‖a-b‖qp where ‖·‖p is the Lp-norm. The geometric partial matching problem asks to find the minimum-cost size-k matching between A and B. We present efficient algorithms for geometric partial matching problem that work for any powers of Lp-norm matching objective: An exact algorithm that runs in O((n + k2) polylog n) time, and a (1 + ε)-approximation algorithm that runs in O((n + k√k) polylog n· log ε−1) time. Both algorithms are based on the primal-dual flow augmentation scheme; the main improvements involve using dynamic data structures to achieve efficient flow augmentations. With similar techniques, we give an exact algorithm for the planar transportation problem running in O(min{n2, rn3/2}polylog n) time.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Chang, HC; Xiao, A

Published Date

  • June 1, 2019

Published In

Volume / Issue

  • 129 /

International Standard Serial Number (ISSN)

  • 1868-8969

International Standard Book Number 13 (ISBN-13)

  • 9783959771047

Digital Object Identifier (DOI)

  • 10.4230/LIPIcs.SoCG.2019.6

Citation Source

  • Scopus