research-article

Online geometric reconstruction

Authors:

Bernard Chazelle,

C. SeshadhriAuthors Info & Claims

Journal of the ACM (JACM), Volume 58, Issue 4

Article No.: 14, Pages 1 - 32

https://doi.org/10.1145/1989727.1989728

Published: 20 July 2011 Publication History

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 (for example, 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.

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Cited By

Gergatsouli ELucier BTzamos CDaumé HSingh A(2020)Black-box methods for restoring monotonicityProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525262(3463-3473)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.5555/3524938.3525262
Berman PMurzabulatov MRaskhodnikova S(2018)Testing convexity of figures under the uniform distributionRandom Structures & Algorithms10.1002/rsa.2079754:3(413-443)Online publication date: 19-Sep-2018
https://doi.org/10.1002/rsa.20797
Levi RRubinfeld RYodpinyanee A(2017)Local Computation Algorithms for Graphs of Non-constant DegreesAlgorithmica10.1007/s00453-016-0126-y77:4(971-994)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1007/s00453-016-0126-y
Show More Cited By

Index Terms

Online geometric reconstruction
1. Theory of computation
  1. Design and analysis of algorithms

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cover image Journal of the ACM

Journal of the ACM Volume 58, Issue 4

July 2011

145 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/1989727

Issue’s Table of Contents

Copyright © 2011 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 20 July 2011

Accepted: 01 April 2011

Revised: 01 December 2010

Received: 01 July 2007

Published in JACM Volume 58, Issue 4

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Cited By

Gergatsouli ELucier BTzamos CDaumé HSingh A(2020)Black-box methods for restoring monotonicityProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525262(3463-3473)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.5555/3524938.3525262
Berman PMurzabulatov MRaskhodnikova S(2018)Testing convexity of figures under the uniform distributionRandom Structures & Algorithms10.1002/rsa.2079754:3(413-443)Online publication date: 19-Sep-2018
https://doi.org/10.1002/rsa.20797
Levi RRubinfeld RYodpinyanee A(2017)Local Computation Algorithms for Graphs of Non-constant DegreesAlgorithmica10.1007/s00453-016-0126-y77:4(971-994)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1007/s00453-016-0126-y
Seshadhri C(2016)Local ReconstructionEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_698(1136-1139)Online publication date: 22-Apr-2016
https://doi.org/10.1007/978-1-4939-2864-4_698
Seshadhri C(2015)Local ReconstructionEncyclopedia of Algorithms10.1007/978-3-642-27848-8_698-1(1-4)Online publication date: 30-Jun-2015
https://doi.org/10.1007/978-3-642-27848-8_698-1
Jha MRaskhodnikova S(2013)Testing and Reconstruction of Lipschitz Functions with Applications to Data PrivacySIAM Journal on Computing10.1137/11084074142:2(700-731)Online publication date: Jan-2013
https://doi.org/10.1137/110840741

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