Bose et al.  asked whether for every simple arrangement of n lines in the plane there exists a simple n-gon P that induces by extending every edge of P into a line. We prove that such a polygon always exists and can be found in O(n logn) time. In fact, we show that every finite family of curves such that every two curves intersect at least once and finitely many times and no three curves intersect at a single point possesses the following Hamiltonian-type property: the union of the curves in contains a simple cycle that visits every curve in exactly once.
|Title of host publication||Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings|
|Number of pages||12|
|State||Published - 2009|
|Event||17th Annual European Symposium on Algorithms, ESA 2009 - Copenhagen, Denmark|
Duration: 7 Sep 2009 → 9 Sep 2009
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||17th Annual European Symposium on Algorithms, ESA 2009|
|Period||7/09/09 → 9/09/09|
Bibliographical noteFunding Information:
Research by Eyal Ackerman was supported by a fellowship from the Alexander von Humboldt Foundation . Research by Rom Pinchasi was supported by the Israeli Science Foundation (grant No. 938/06 ).
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)