The complexity of separating points in the plane

Cabello, Sergio and Giannopoulos, Panos (2016) The complexity of separating points in the plane. Algorithmica, 74 (2). pp. 643-663. ISSN 0178-4617

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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.

Item Type: Article
Additional Information: First online: 30 December 2014
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 16041
Notes on copyright: 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
Depositing User: Panos Giannopoulos
Date Deposited: 15 May 2015 14:23
Last Modified: 02 Apr 2019 19:11
URI: https://eprints.mdx.ac.uk/id/eprint/16041

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