TY - GEN

T1 - Translating a planar object to maximize point containment

AU - Agarwal, Pankaj K.

AU - Hagerup, Torben

AU - Ray, Rahul

AU - Sharir, Micha

AU - Smid, Michiel

AU - Welzl, Emo

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

PY - 2002

Y1 - 2002

N2 - bet C be a compact set in R2 and let S be a set of n points in R2. We consider the problem of computing a translate of C that contains the maximum number, K*, of pointsof S. It is known that this problem can be solved in a time that is roughly quadratic in n.We show how random-sampling and bucketing techniques can be used to develop a near-linear-time Monte Carlo algorithm that computes a placement of C containing at least (1 — ε)K* points of S, for given ε> 0, with high probability. We also present a deterministic algorithm that solves the ε-approximate version of the optimal-placement problem and runs in O((n1+δ+ n/ε)logm) time, for arbitrary constant δ> 0, if C is a convex m-gon.

AB - bet C be a compact set in R2 and let S be a set of n points in R2. We consider the problem of computing a translate of C that contains the maximum number, K*, of pointsof S. It is known that this problem can be solved in a time that is roughly quadratic in n.We show how random-sampling and bucketing techniques can be used to develop a near-linear-time Monte Carlo algorithm that computes a placement of C containing at least (1 — ε)K* points of S, for given ε> 0, with high probability. We also present a deterministic algorithm that solves the ε-approximate version of the optimal-placement problem and runs in O((n1+δ+ n/ε)logm) time, for arbitrary constant δ> 0, if C is a convex m-gon.

UR - http://www.scopus.com/inward/record.url?scp=84938067527&partnerID=8YFLogxK

U2 - 10.1007/3-540-45749-6_8

DO - 10.1007/3-540-45749-6_8

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AN - SCOPUS:84938067527

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 42

EP - 53

BT - Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings

A2 - Möhring, Rolf

A2 - Raman, Rajeev

PB - Springer Verlag

T2 - 10th Annual European Symposium on Algorithms, ESA 2002

Y2 - 17 September 2002 through 21 September 2002

ER -