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Dynamic Ray Stabbing

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Yufei TaoAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 11, Issue 2

Article No.: 11, Pages 1 - 19

https://doi.org/10.1145/2559153

Published: 30 October 2014 Publication History

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Abstract

We consider maintaining a dynamic set S of N horizontal segments in ℝ² such that, given a vertical ray Q in ℝ², the segments in S intersecting Q can be reported efficiently. In the external memory model, we give a structure that consumes O(N/B) space, answers a query in O(log _BN + K/B) time (where K is the number of reported segments), and can be updated in O(log _BN) amortized time per insertion and deletion. With B set to a constant, the structure also works in internal memory, consuming space O(N), answering a query in O(log N + K) time, and supporting an update in O(log N) amortized time.

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Cited By

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Cao BHou CFan JLim EWinslett MSanderson MFu ASun JCulpepper SLo EHo JDonato DAgrawal RZheng YCastillo CSun ATseng VLi C(2017)Covering the Optimal Time Window Over Temporal DataProceedings of the 2017 ACM on Conference on Information and Knowledge Management10.1145/3132847.3132935(687-696)Online publication date: 6-Nov-2017
https://dl.acm.org/doi/10.1145/3132847.3132935
Navarro GThankachan S(2015)Reporting Consecutive Substring Occurrences Under Bounded Gap ConstraintsCombinatorial Pattern Matching10.1007/978-3-319-19929-0_31(367-373)Online publication date: 16-Jun-2015
https://doi.org/10.1007/978-3-319-19929-0_31

Index Terms

Dynamic Ray Stabbing
1. Theory of computation
  1. Randomness, geometry and discrete structures

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We consider maintaining a dynamic set S of N horizontal segments in R² such that, given a vertical ray Q in R², the segments in S intersecting Q can be reported efficiently. In the external memory model, we give a structure that consumes O(N/B) space, ...
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In this paper we present new space efficient dynamic data structures for orthogonal range reporting. The described data structures support planar range reporting queries in time O(log n+klog log (4n/(k+1))) and space O(nlog log n), or in time O(log n+k) ...

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 11, Issue 2

November 2014

215 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2685353

Editor:
Aravind Srinivasan
University of Maryland, USA

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Association for Computing Machinery

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Publication History

Published: 30 October 2014

Accepted: 01 November 2013

Received: 01 August 2012

Published in TALG Volume 11, Issue 2

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Cao BHou CFan JLim EWinslett MSanderson MFu ASun JCulpepper SLo EHo JDonato DAgrawal RZheng YCastillo CSun ATseng VLi C(2017)Covering the Optimal Time Window Over Temporal DataProceedings of the 2017 ACM on Conference on Information and Knowledge Management10.1145/3132847.3132935(687-696)Online publication date: 6-Nov-2017
https://dl.acm.org/doi/10.1145/3132847.3132935
Navarro GThankachan S(2015)Reporting Consecutive Substring Occurrences Under Bounded Gap ConstraintsCombinatorial Pattern Matching10.1007/978-3-319-19929-0_31(367-373)Online publication date: 16-Jun-2015
https://doi.org/10.1007/978-3-319-19929-0_31

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Stabbing horizontal segments with vertical rays

Towards an Optimal Method for Dynamic Planar Point Location

Space Efficient Dynamic Orthogonal Range Reporting

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Stabbing horizontal segments with vertical rays

Towards an Optimal Method for Dynamic Planar Point Location

Space Efficient Dynamic Orthogonal Range Reporting

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