Translating a planar object to maximize point containment

Pankaj K. Agarwal, Torben Hagerup, Rahul Ray, Micha Sharir, Michiel Smid, Emo Welzl

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationAlgorithms - ESA 2002 - 10th Annual European Symposium, Proceedings
EditorsRolf Möhring, Rajeev Raman
PublisherSpringer Verlag
Number of pages12
ISBN (Electronic)3540441808, 9783540441809
StatePublished - 2002
Event10th Annual European Symposium on Algorithms, ESA 2002 - Rome, Italy
Duration: 17 Sep 200221 Sep 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference10th Annual European Symposium on Algorithms, ESA 2002


FundersFunder number
National Science FoundationCCR-00-86013, CCR-00-98246, ITR-333-1050, CCR-9732787, EIA-9870724, CCR-97-32101, EIA-9972879


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