Online geometric reconstruction

Bernard Chazelle, C. Seshadhri

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

6 Scopus citations

Abstract

We investigate a new class of geometric problems based on the idea of online error correction. Suppose one is given access to a large geometric dataset though a query mechanism; for example, the dataset could be a terrain and a query might ask for the coordinates of a particular vertex or for the edges incident to it. Suppose, in addition, that the dataset satisfies some known structural property P (eg, monotonicity or convexity) but that, because of errors and noise, the queries occasionally provide answers that violate P. Can one design a filter that modifies the query's answers so that (i) the output satisfies P; (ii) the amount of data modification is minimized? We provide upper and lower bounds on the complexity of online reconstruction for convexity in 2D and 3D.

Original languageEnglish (US)
Title of host publicationProceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06
PublisherAssociation for Computing Machinery
Pages386-394
Number of pages9
ISBN (Print)1595933409, 9781595933409
DOIs
StatePublished - 2006
Event22nd Annual Symposium on Computational Geometry 2006, SCG'06 - Sedona, AZ, United States
Duration: Jun 5 2006Jun 7 2006

Publication series

NameProceedings of the Annual Symposium on Computational Geometry
Volume2006

Other

Other22nd Annual Symposium on Computational Geometry 2006, SCG'06
CountryUnited States
CitySedona, AZ
Period6/5/066/7/06

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Keywords

  • Computational Geometry
  • Sublinear algorithms

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  • Cite this

    Chazelle, B., & Seshadhri, C. (2006). Online geometric reconstruction. In Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06 (pp. 386-394). (Proceedings of the Annual Symposium on Computational Geometry; Vol. 2006). Association for Computing Machinery. https://doi.org/10.1145/1137856.1137912