Lars Arge

Improved dynamic geodesic nearest neighbor searching in a simple polygon

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

Standard

Improved dynamic geodesic nearest neighbor searching in a simple polygon. / Agarwal, Pankaj K.; Arge, Lars; Staals, Frank.

34th International Symposium on Computational Geometry, SoCG 2018. ed. / Csaba D. Toth; Bettina Speckmann. Vol. 99 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. p. 4:1-4:14 (Leibniz International Proceedings in Informatics, Vol. 99).

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

Harvard

Agarwal, PK, Arge, L & Staals, F 2018, Improved dynamic geodesic nearest neighbor searching in a simple polygon. in CD Toth & B Speckmann (eds), 34th International Symposium on Computational Geometry, SoCG 2018. vol. 99, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Leibniz International Proceedings in Informatics, vol. 99, pp. 4:1-4:14, 34th International Symposium on Computational Geometry, SoCG 2018, Budapest, Hungary, 11/06/2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.4

APA

Agarwal, P. K., Arge, L., & Staals, F. (2018). Improved dynamic geodesic nearest neighbor searching in a simple polygon. In C. D. Toth, & B. Speckmann (Eds.), 34th International Symposium on Computational Geometry, SoCG 2018 (Vol. 99, pp. 4:1-4:14). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. Leibniz International Proceedings in Informatics, Vol.. 99 https://doi.org/10.4230/LIPIcs.SoCG.2018.4

CBE

Agarwal PK, Arge L, Staals F. 2018. Improved dynamic geodesic nearest neighbor searching in a simple polygon. Toth CD, Speckmann B, editors. In 34th International Symposium on Computational Geometry, SoCG 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. pp. 4:1-4:14. (Leibniz International Proceedings in Informatics, Vol. 99). https://doi.org/10.4230/LIPIcs.SoCG.2018.4

MLA

Agarwal, Pankaj K., Lars Arge and Frank Staals "Improved dynamic geodesic nearest neighbor searching in a simple polygon". and Toth, Csaba D. Speckmann, Bettina (editors). 34th International Symposium on Computational Geometry, SoCG 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. (Leibniz International Proceedings in Informatics, Vol. 99). 2018, 4:1-4:14. https://doi.org/10.4230/LIPIcs.SoCG.2018.4

Vancouver

Agarwal PK, Arge L, Staals F. Improved dynamic geodesic nearest neighbor searching in a simple polygon. In Toth CD, Speckmann B, editors, 34th International Symposium on Computational Geometry, SoCG 2018. Vol. 99. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. p. 4:1-4:14. (Leibniz International Proceedings in Informatics, Vol. 99). https://doi.org/10.4230/LIPIcs.SoCG.2018.4

Author

Agarwal, Pankaj K. ; Arge, Lars ; Staals, Frank. / Improved dynamic geodesic nearest neighbor searching in a simple polygon. 34th International Symposium on Computational Geometry, SoCG 2018. editor / Csaba D. Toth ; Bettina Speckmann. Vol. 99 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. pp. 4:1-4:14 (Leibniz International Proceedings in Informatics, Vol. 99).

Bibtex

@inproceedings{d322adb0e98545e885e626b6afaa8783,
title = "Improved dynamic geodesic nearest neighbor searching in a simple polygon",
abstract = "We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set S of point sites in a static simple polygon P. Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q ∈ P. All distances are measured using the geodesic distance, that is, the length of the shortest path that is completely contained in P. Our data structure achieves polylogarithmic update and query times, and uses O(n log3 nlog m + m) space, where n is the number of sites in S and m is the number of vertices in P. The crucial ingredient in our data structure is an implicit representation of a vertical shallow cutting of the geodesic distance functions. We show that such an implicit representation exists, and that we can compute it efficiently.",
keywords = "Data structure, Geodesic distance, Nearest neighbor searching, Shallow cutting, Simple polygon",
author = "Agarwal, {Pankaj K.} and Lars Arge and Frank Staals",
year = "2018",
doi = "10.4230/LIPIcs.SoCG.2018.4",
language = "English",
volume = "99",
series = "Leibniz International Proceedings in Informatics",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "4:1--4:14",
editor = "Toth, {Csaba D.} and Bettina Speckmann",
booktitle = "34th International Symposium on Computational Geometry, SoCG 2018",
note = "34th International Symposium on Computational Geometry, SoCG 2018 ; Conference date: 11-06-2018 Through 14-06-2018",

}

RIS

TY - GEN

T1 - Improved dynamic geodesic nearest neighbor searching in a simple polygon

AU - Agarwal, Pankaj K.

AU - Arge, Lars

AU - Staals, Frank

PY - 2018

Y1 - 2018

N2 - We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set S of point sites in a static simple polygon P. Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q ∈ P. All distances are measured using the geodesic distance, that is, the length of the shortest path that is completely contained in P. Our data structure achieves polylogarithmic update and query times, and uses O(n log3 nlog m + m) space, where n is the number of sites in S and m is the number of vertices in P. The crucial ingredient in our data structure is an implicit representation of a vertical shallow cutting of the geodesic distance functions. We show that such an implicit representation exists, and that we can compute it efficiently.

AB - We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set S of point sites in a static simple polygon P. Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q ∈ P. All distances are measured using the geodesic distance, that is, the length of the shortest path that is completely contained in P. Our data structure achieves polylogarithmic update and query times, and uses O(n log3 nlog m + m) space, where n is the number of sites in S and m is the number of vertices in P. The crucial ingredient in our data structure is an implicit representation of a vertical shallow cutting of the geodesic distance functions. We show that such an implicit representation exists, and that we can compute it efficiently.

KW - Data structure

KW - Geodesic distance

KW - Nearest neighbor searching

KW - Shallow cutting

KW - Simple polygon

UR - http://www.scopus.com/inward/record.url?scp=85048971454&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SoCG.2018.4

DO - 10.4230/LIPIcs.SoCG.2018.4

M3 - Article in proceedings

AN - SCOPUS:85048971454

VL - 99

T3 - Leibniz International Proceedings in Informatics

SP - 4:1-4:14

BT - 34th International Symposium on Computational Geometry, SoCG 2018

A2 - Toth, Csaba D.

A2 - Speckmann, Bettina

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 34th International Symposium on Computational Geometry, SoCG 2018

Y2 - 11 June 2018 through 14 June 2018

ER -