Numerical stability of algorithms for line arrangements

Steven Fortune, Victor Milenkovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

23 Scopus citations

Abstract

We analyze the behavior of two line arrangement algorithms, a sweepline algorithm and an incremental algorithm, in approximate arithmetic. The algorithms have running times O(n2 log n) and O(n2) respectively. We show that each of these algorithms can be implemented to have O(n∈) relative error. This means that each algorithm produces an arrangement realized by a set of pseudolines so that each pseudoline differs from the corresponding line relatively by at most O(n∈). We also show that there is a line arrangement algorithm with O(n2 log n) running time and O(∈) relative error.

Original languageEnglish (US)
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery
Pages334-341
Number of pages8
VolumePart F129851
ISBN (Print)0897914260
DOIs
StatePublished - Jun 1 1991
Externally publishedYes
Event7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States
Duration: Jun 10 1991Jun 12 1991

Other

Other7th Annual Symposium on Computational Geometry, SCG 1991
CountryUnited States
CityNorth Conway
Period6/10/916/12/91

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Fortune, S., & Milenkovic, V. (1991). Numerical stability of algorithms for line arrangements. In Proceedings of the Annual Symposium on Computational Geometry (Vol. Part F129851, pp. 334-341). Association for Computing Machinery. https://doi.org/10.1145/109648.109685