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. 643663. ISSN 01784617

PDF
 Final accepted version (with author's formatting)
Download (670kB)  Preview 
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 3pathcondition, and arguing that a shortest cycle in the family gives an optimal solution. The 3pathcondition 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 NPhard 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 postprint 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/s0045301499656 
Useful Links:  
Depositing User:  Panos Giannopoulos 
Date Deposited:  15 May 2015 14:23 
Last Modified:  08 Sep 2018 22:37 
URI:  http://eprints.mdx.ac.uk/id/eprint/16041 
Actions (login required)
Edit Item 
Full text downloads (NB count will be zero if no full text documents are attached to the record)
Downloads per month over the past year