License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.89
URN: urn:nbn:de:0030-drops-90937
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9093/
Barequet, Gill ;
Eppstein, David ;
Goodrich, Michael T. ;
Mamano, Nil
Stable-Matching Voronoi Diagrams: Combinatorial Complexity and Algorithms
Abstract
We study algorithms and combinatorial complexity bounds for stable-matching Voronoi diagrams, where a set, S, of n point sites in the plane determines a stable matching between the points in R^2 and the sites in S such that (i) the points prefer sites closer to them and sites prefer points closer to them, and (ii) each site has a quota indicating the area of the set of points that can be matched to it. Thus, a stable-matching Voronoi diagram is a solution to the classic post office problem with the added (realistic) constraint that each post office has a limit on the size of its jurisdiction. Previous work provided existence and uniqueness proofs, but did not analyze its combinatorial or algorithmic complexity. We show that a stable-matching Voronoi diagram of n sites has O(n^{2+epsilon}) faces and edges, for any epsilon>0, and show that this bound is almost tight by giving a family of diagrams with Theta(n^2) faces and edges. We also provide a discrete algorithm for constructing it in O(n^3+n^2f(n)) time, where f(n) is the runtime of a geometric primitive that can be performed in the real-RAM model or can be approximated numerically. This is necessary, as the diagram cannot be computed exactly in an algebraic model of computation.
BibTeX - Entry
@InProceedings{barequet_et_al:LIPIcs:2018:9093,
author = {Gill Barequet and David Eppstein and Michael T. Goodrich and Nil Mamano},
title = {{Stable-Matching Voronoi Diagrams: Combinatorial Complexity and Algorithms}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {89:1--89:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-076-7},
ISSN = {1868-8969},
year = {2018},
volume = {107},
editor = {Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9093},
URN = {urn:nbn:de:0030-drops-90937},
doi = {10.4230/LIPIcs.ICALP.2018.89},
annote = {Keywords: Voronoi diagram, stable matching, combinatorial complexity, lower bounds}
}
Keywords: |
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Voronoi diagram, stable matching, combinatorial complexity, lower bounds |
Collection: |
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45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) |
Issue Date: |
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2018 |
Date of publication: |
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04.07.2018 |