Minimum cell connection in line segment arrangements

Alt, Helmut and Cabello, Sergio and Giannopoulos, Panos and Knauer, Christian (2017) Minimum cell connection in line segment arrangements. International Journal of Computational Geometry and Applications, 27 (3). pp. 159-176. ISSN 1793-6357

[img]
Preview
PDF - Final accepted version (with author's formatting)
Download (389kB) | Preview

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.

Item Type: Article
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 16045
Notes on copyright: 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
Useful Links:
Depositing User: Panos Giannopoulos
Date Deposited: 15 May 2015 14:26
Last Modified: 07 Sep 2018 11:06
URI: http://eprints.mdx.ac.uk/id/eprint/16045

Actions (login required)

Edit Item 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