Article

Online geometric reconstruction

Authors:

Bernard Chazelle,

C. SeshadhriAuthors Info & Claims

SCG '06: Proceedings of the twenty-second annual symposium on Computational geometry

Pages 386 - 394

https://doi.org/10.1145/1137856.1137912

Published: 05 June 2006 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 (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.

References

[1]

Alon, N., Spencer, J. The probabilistic method, John Wiley, 2nd edition, 2000.]]

[2]

Agarwal, P.K., Desikan P.K. An efficient algorithm for terrain simplification, Proc. SODA (1997), 139--147.]]

Digital Library

[3]

Agarwal, P.K., Hagerup, T., Ray, R., Sharir, M., Smid, M., Welzl, E. Translating a planar object to maximize point containment, Proc. ESA (2002), 42--53.]]

Digital Library

[4]

Agarwal, P.K., Har-Peled, S., Mustafa, N., Wang, Y. Near-linear time approximation algorithms for curve simplification, to appear in Algorithmica.]]

Digital Library

[5]

Agarwal, P.K., Matoušek, J. Dynamic half-space searching and its applications, Algorithmica 14 (1995), 325--345.]]

[6]

Agarwal, P.K., Suri, S. Surface approximation and geometric partitions, SIAM J. Computing 27 (1998), 1016--1035.]]

Digital Library

[7]

Ailon, N., Chazelle, B., Comandur, S., Liu, D. Estimating the distance to a monotone function, Proc. RANDOM (2004), 229--236.]]

[8]

Ailon, N., Chazelle, B., Comandur, S., Liu, D. Property preserving data reconstruction, Proc. ISAAC (2004), 16--27.]]

Digital Library

[9]

Alon, N., Dar, S., Parnas, M., Ron, D. Testing of clustering, Proc. FOCS (2000), 240--250.]]

Digital Library

[10]

Amenta, N., Choi, S., Dey, T.K., Leekha, N. A simple algorithm for homeomorphic surface reconstruction Proc. SOCG (2000), 213--222.]]

Digital Library

[11]

Chazelle, B. The Discrepancy Method : Randomness and Complexity, Cambridge University Press, 2000; paperback version, 2001.]]

Digital Library

[12]

Chazelle, B., Liu, D., Magen, A. Sublinear geometric algorithms, Proc. STOC (2003), 531--540.]]

Digital Library

[13]

Chvatal, V., Klincsek, G. Finding largest convex subsets, Congressus Numerantium: 29 (1980), 453--460.]]

[14]

Czumaj, A., Ergun, F., Fortnow, L., Magen, A., Newman, I., Rubinfeld, R., Sohler, C., Sublinear-time approximation of Euclidean minimum spanning tree, Proc. SODA (2003), 813--822.]]

Digital Library

[15]

Czumaj, A., Sohler, C. Property testing with geometric queries, Proc. ESA (2001), 266--277.]]

Digital Library

[16]

Czumaj, A., Sohler, C. Estimating the weight of metric minimum spanning trees in sublinear-time, Proc. STOC (2004), 175--183.]]

Digital Library

[17]

Czumaj, A., Sohler, C., Ziegler M. Property testing in computational geometry, Proc. ESA (2000), 155--166.]]

Digital Library

[18]

de Berg, M., van Kreveld, M., Overmars, O., Schwarzkopf, O. Computational Geometry - Algorithms and Applications, Springer-Verlag, 1997.]]

Digital Library

[19]

Ergun, F., Kannan, S., Kumar, S. Ravi, Rubinfeld, R., Viswanathan, M. Spot-checkers, Proc. STOC (1998), 259--268.]]

Digital Library

[20]

Frederickson, G.N. Fast algorithms for shortest paths in planar graphs, with applications, SIAM J. Comput. 16 (1987), 1004--1022.]]

Digital Library

[21]

Indyk, P. A sublinear-time approximation scheme for clustering in metric spaces, Proc. FOCS (1999), 154--159.]]

Digital Library

[22]

Indyk, P. Sublinear-time algorithms for metric space problems, Proc. STOC 1999, 428--434.]]

Digital Library

[23]

Lipton, R.J., Tarjan, R.E. A separator theorem for planar graphs, SIAM Journal on Applied Mathematics 36 (1979), 177--189.]]

Digital Library

[24]

Lipton, R.J., Tarjan, R.E. Applications of a planar separator theorem, SIAM J. Comput. 9 (1980), 615--627.]]

Digital Library

[25]

Mehlhorn, K., Näher, S., Seel, M., Seidel, R., Schilz, T., Schirra, S., Uhrig, C. Checking geometric programs or verification of geometric structures, Proc. SOCG (1996), 159--165.]]

Digital Library

[26]

Miller, G.L. Finding small simple cycle separators for 2-connected planar graphs, J. Computer and System Sciences 32 (1986), 265--279.]]

Digital Library

[27]

Mishra, N., Oblinger, D., Pitt, L. Sublinear time approximate clustering, Proc. SODA (2001), 439--447.]]

Digital Library

Cited By

Levi RRon DRubinfeld R(2019)Local Algorithms for Sparse Spanning GraphsAlgorithmica10.1007/s00453-019-00612-6Online publication date: 3-Aug-2019
https://doi.org/10.1007/s00453-019-00612-6
Levi RMoshkovitz GRon DRubinfeld RShapira A(2016)Constructing near spanning trees with few local inspectionsRandom Structures & Algorithms10.1002/rsa.2065250:2(183-200)Online publication date: 4-Apr-2016
https://doi.org/10.1002/rsa.20652
Campagna AGuo ARubinfeld R(2013)Local Reconstructors and Tolerant Testers for Connectivity and DiameterApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques10.1007/978-3-642-40328-6_29(411-424)Online publication date: 2013
https://doi.org/10.1007/978-3-642-40328-6_29
Show More Cited By

Index Terms

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

Recommendations

Online geometric reconstruction

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 ...
Range-aggregate query problems involving geometric aggregation operations

We consider variations of the standard orthogonal range searching motivated by applications in database querying and VLSI layout processing. In a generic instance of such a problem, called a range-aggregate query problem we wish to preprocess a set S of ...
Range-aggregate queries for geometric extent problems
CATS '13: Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141

Let S be a set of n points in the plane. We present data structures that solve range-aggregate query problems on three geometric extent measure problems. Using these data structures, we can report, for any axis-parallel query rectangle Q, the area/...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

SCG '06: Proceedings of the twenty-second annual symposium on Computational geometry

June 2006

500 pages

ISBN:1595933409

DOI:10.1145/1137856

Program Chairs:
Nina Amenta
University of California at Davis
,
Otfried Cheong
Korea Advanced Institute of Science and Technology

Copyright © 2006 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]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 June 2006

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

SoCG06

Sponsor:

SoCG06: 22nd Annual Symposium on Computational Geometry

June 5 - 7, 2006

Arizona, Sedona, USA

Acceptance Rates

Overall Acceptance Rate 625 of 1,685 submissions, 37%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
234
Total Downloads

Downloads (Last 12 months)2
Downloads (Last 6 weeks)0

Reflects downloads up to 02 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

Levi RRon DRubinfeld R(2019)Local Algorithms for Sparse Spanning GraphsAlgorithmica10.1007/s00453-019-00612-6Online publication date: 3-Aug-2019
https://doi.org/10.1007/s00453-019-00612-6
Levi RMoshkovitz GRon DRubinfeld RShapira A(2016)Constructing near spanning trees with few local inspectionsRandom Structures & Algorithms10.1002/rsa.2065250:2(183-200)Online publication date: 4-Apr-2016
https://doi.org/10.1002/rsa.20652
Campagna AGuo ARubinfeld R(2013)Local Reconstructors and Tolerant Testers for Connectivity and DiameterApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques10.1007/978-3-642-40328-6_29(411-424)Online publication date: 2013
https://doi.org/10.1007/978-3-642-40328-6_29
Alon NRubinfeld RVardi SXie N(2012)Space-efficient local computation algorithmsProceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms10.5555/2095116.2095205(1132-1139)Online publication date: 17-Jan-2012
https://dl.acm.org/doi/10.5555/2095116.2095205
Jha MRaskhodnikova S(2011)Testing and Reconstruction of Lipschitz Functions with Applications to Data PrivacyProceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science10.1109/FOCS.2011.13(433-442)Online publication date: 22-Oct-2011
https://dl.acm.org/doi/10.1109/FOCS.2011.13
Kale SPeres YSeshadhri C(2008)Noise Tolerance of Expanders and Sublinear Expander ReconstructionProceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science10.1109/FOCS.2008.65(719-728)Online publication date: 25-Oct-2008
https://dl.acm.org/doi/10.1109/FOCS.2008.65

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents