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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.

References

[1]

Pankaj K. Agarwal, Siu-Wing Cheng, Yufei Tao, and Ke Yi. 2009. Indexing uncertain data. In Proceedings of ACM Symposium on Principles of Database Systems (PODS'09). 137--146.

Digital Library

Google Scholar

[2]

Alok Aggarwal and Jeffrey Scott Vitter. 1988. The input/output complexity of sorting and related problems. Communications of the ACM 31, 9 (1988), 1116--1127.

Digital Library

Google Scholar

[3]

Lars Arge, Vasilis Samoladas, and Jeffrey Scott Vitter. 1999. On two-dimensional indexability and optimal range search indexing. In Proceedings of ACM Symposium on Principles of Database Systems (PODS'99). 346--357.

Digital Library

Google Scholar

[4]

Lars Arge and Jeffrey Scott Vitter. 2003. Optimal external memory interval management. SIAM Journal of Computing 32, 6 (2003), 1488--1508.

Digital Library

Google Scholar

[5]

Bruno Becker, Stephan Gschwind, Thomas Ohler, Bernhard Seeger, and Peter Widmayer. 1996. An asymptotically optimal multiversion b-tree. VLDB Journal 5, 4 (1996), 264--275.

Digital Library

Google Scholar

[6]

Elisa Bertino, Barbara Catania, and Boris Shidlovsky. 1998. Towards optimal indexing for segment databases. In Proceedings of Extending Database Technology (EDBT'98). 39--53.

Digital Library

Google Scholar

[7]

Guy E. Blelloch. 2008. Space-efficient dynamic orthogonal point location, segment intersection, and range reporting. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'08). 894--903.

Digital Library

Google Scholar

[8]

Bernard Chazelle. 1986. Filtering search: A new approach to query-answering. SIAM Journal of Computing 15, 3 (1986), 703--724.

Digital Library

Google Scholar

[9]

Siu-Wing Cheng and Ravi Janardan. 1990. Efficient dynamic algorithms for some geometric intersection problems. Information Processing Letters 36, 5 (1990), 251--258.

Digital Library

Google Scholar

[10]

Jost Enderle, Nicole Schneider, and Thomas Seidl. 2005. Efficiently processing queries on interval-and-value tuples in relational databases. In Proceedings of Very Large Data Bases (VLDB'05). 385--396.

Digital Library

Google Scholar

[11]

Michael T. Goodrich, Jyh-Jong Tsay, Darren Erik Vengroff, and Jeffrey Scott Vitter. 1993. External-memory computational geometry. In Proceedings of Annual IEEE Symposium on Foundations of Computer Science (FOCS'93). 714--723.

Digital Library

Google Scholar

[12]

Haim Kaplan, Eyal Molad, and Robert Endre Tarjan. 2003. Dynamic rectangular intersection with priorities. In Proceedings of ACM Symposium on Theory of Computing (STOC). 639--648.

Digital Library

Google Scholar

[13]

Christian Worm Mortensen. 2003. Fully-dynamic two dimensional orthogonal range and line segment intersection reporting in logarithmic time. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'03). 618--627.

Digital Library

Google Scholar

[14]

Betty Salzberg and Vassilis J. Tsotras. 1999. Comparison of access methods for time-evolving data. Computer Surveys 31, 2 (1999), 158--221.

Digital Library

Google Scholar

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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