License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.09111.6
URN: urn:nbn:de:0030-drops-20292
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/2029/
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Rote, Günter

Two Applications of Point Matching

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09111.RoteGuenter.ExtAbstract.2029.pdf (0.2 MB)

Abstract

The two following problems can be solved by a reduction
to a minimum-weight bipartite matching problem (or a related
network flow problem):

a) Floodlight illumination:
We are given $n$ infinite wedges (sectors, spotlights) that can cover
the whole plane when placed at the origin.
They are to be assigned to $n$ given locations
(in arbitrary order, but without rotation)
such that they still cover the whole plane.
(This extends results of Bose et al. from 1997.)

b) Convex partition:
Partition a convex $m$-gon into $m$ convex parts, each part
containing one of the edges and a given number of points from a given
point set. (Garcia and Tejel 1995, Aurenhammer 2008)

BibTeX - Entry

@InProceedings{rote:DagSemProc.09111.6,
  author =	{Rote, G\"{u}nter},
  title =	{{Two Applications of Point Matching}},
  booktitle =	{Computational Geometry},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9111},
  editor =	{Pankaj Kumar Agarwal and Helmut Alt and Monique Teillaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2009/2029},
  URN =		{urn:nbn:de:0030-drops-20292},
  doi =		{10.4230/DagSemProc.09111.6},
  annote =	{Keywords: Bipartite matching, least-squares}
}

Keywords: Bipartite matching, least-squares
Collection: 09111 - Computational Geometry
Issue Date: 2009
Date of publication: 24.06.2009

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