Minimum cell connection in line segment arrangements

Article


Alt, H., Cabello, S., Giannopoulos, P. and Knauer, C. 2017. Minimum cell connection in line segment arrangements. International Journal of Computational Geometry and Applications. 27 (3), pp. 159-176. https://doi.org/10.1142/s0218195917500017
TypeArticle
TitleMinimum cell connection in line segment arrangements
AuthorsAlt, H., Cabello, S., Giannopoulos, P. and Knauer, C.
Abstract

We study the complexity of the following cell connection problems in segment arrangements. Given a set of straight-line segments in the plane and two points a and b in different cells of the induced arrangement:
(i) compute the minimum number of segments one needs to remove so that there is a path connecting a to b that does not intersect any of the remaining segments;
(ii) compute the minimum number of segments one needs to remove so that the arrangement induced by the remaining segments has a single cell.
We show that problems (i) and (ii) are NP-hard and discuss some special, tractable cases. Most notably, we provide a near-linear-time algorithm for a variant of problem (i) where the path connecting a to b must stay inside a given polygon P with a constant number of holes, the segments are contained in P, and the endpoints of the segments are on the boundary of P. The approach for this latter result uses homotopy of paths to group the segments into clusters with the property that either all segments in a cluster or none participate in an optimal solution.

Research GroupFoundations of Computing group
LanguageEnglish
PublisherWorld Scientific Publishing
JournalInternational Journal of Computational Geometry and Applications
ISSN0218-1959
Electronic1793-6357
Publication dates
Print01 Sep 2017
Online31 Jan 2018
Publication process dates
Deposited15 May 2015
Submitted27 Dec 2012
Accepted25 Apr 2016
Output statusPublished
Accepted author manuscript
Copyright Statement

Publisher permits use of author's corrected copy.
Electronic version of an article published as Minimum Cell Connection in Line Segment Arrangements, Helmut Alt, Sergio Cabello, Panos Giannopoulos, and Christian Knauer,
International Journal of Computational Geometry & Applications 2017 27:03, 159-176, https://doi.org/10.1142/S0218195917500017 © [copyright World Scientific Publishing Company] http://www.worldscientific.com/worldscinet/ijcga

Digital Object Identifier (DOI)https://doi.org/10.1142/s0218195917500017
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