TY - GEN

T1 - Online geometric reconstruction

AU - Chazelle, Bernard

AU - Seshadhri, C.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Computational Geometry

KW - Sublinear algorithms

UR - http://www.scopus.com/inward/record.url?scp=33748063607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748063607&partnerID=8YFLogxK

U2 - 10.1145/1137856.1137912

DO - 10.1145/1137856.1137912

M3 - Conference contribution

SN - 1595933409

SN - 9781595933409

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 386

EP - 394

BT - Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06

PB - Association for Computing Machinery

T2 - 22nd Annual Symposium on Computational Geometry 2006, SCG'06

Y2 - 5 June 2006 through 7 June 2006

ER -