The complexity of separating points in the plane

Article


Cabello, S. and Giannopoulos, P. 2016. The complexity of separating points in the plane. Algorithmica. 74 (2), pp. 643-663. https://doi.org/10.1007/s00453-014-9965-6
TypeArticle
TitleThe complexity of separating points in the plane
AuthorsCabello, S. and Giannopoulos, P.
Abstract

We study the following separation problem: given n connected curves and two points s and t in the plane, compute the minimum number of curves one needs to retain so that any path connecting s to t intersects some of the retained curves. We give the first polynomial (O(n3)) time algorithm for the problem, assuming that the curves have reasonable computational properties. The algorithm is based on considering the intersection graph of the curves, defining an appropriate family of closed walks in the intersection graph that satisfies the 3-path-condition, and arguing that a shortest cycle in the family gives an optimal solution. The 3-path-condition has been used mainly in topological graph theory, and thus its use here makes the connection to topology clear. We also show that the generalized version, where several input points are to be separated, is NP-hard for natural families of curves, like segments in two directions or unit circles.

Research GroupFoundations of Computing group
PublisherSpringer
JournalAlgorithmica
ISSN0178-4617
Publication dates
PrintFeb 2016
Publication process dates
Deposited15 May 2015
Accepted16 Dec 2014
Output statusPublished
Accepted author manuscript
Copyright Statement

Author's post-print may be made available on any open access repository after 12 months after publication. The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-014-9965-6

Additional information

First online: 30 December 2014

Digital Object Identifier (DOI)https://doi.org/10.1007/s00453-014-9965-6
LanguageEnglish
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https://repository.mdx.ac.uk/item/85552

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