Routing in polygonal domains

Bahareh Banyassady; Man Kwun Chiu; Matias Korman; Wolfgang Mulzer; André Van Renssen; Marcel Roeloffzen; Paul Seiferth; Yannik Stein; Birgit Vogtenhuber; Max Willert

doi:10.4230/LIPIcs.ISAAC.2017.10

Routing in polygonal domains

Bahareh Banyassady, Man Kwun Chiu, Matias Korman, Wolfgang Mulzer, André Van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein, Birgit Vogtenhuber, Max Willert

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of P, where each step must use only the label of the target node q and the routing table of the current node. For any fixed ϵ > 0, we present a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + ϵ. The labels have O(log n) bits, and the routing tables are of size O((ϵ^-1+h) log n). The preprocessing time is O(n² log n+hn²+ ϵ^-1hn). It can be improved to O(n² + ϵ^-1n) for simple polygons.

Original language	English
Title of host publication	28th International Symposium on Algorithms and Computation, ISAAC 2017
Editors	Takeshi Tokuyama, Yoshio Okamoto
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959770545
DOIs	https://doi.org/10.4230/LIPIcs.ISAAC.2017.10
Publication status	Published - 2017 Dec 1
Event	28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand Duration: 2017 Dec 9 → 2017 Dec 22

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	92
ISSN (Print)	1868-8969

Other

Other	28th International Symposium on Algorithms and Computation, ISAAC 2017
Country/Territory	Thailand
City	Phuket
Period	17/12/9 → 17/12/22

Keywords

Polygonal domains
Routing scheme
Small stretch
Yao graph

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.ISAAC.2017.10

Cite this

Banyassady, B., Chiu, M. K., Korman, M., Mulzer, W., Van Renssen, A., Roeloffzen, M., Seiferth, P., Stein, Y., Vogtenhuber, B., & Willert, M. (2017). Routing in polygonal domains. In T. Tokuyama, & Y. Okamoto (Eds.), 28th International Symposium on Algorithms and Computation, ISAAC 2017 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2017.10

Routing in polygonal domains. / Banyassady, Bahareh; Chiu, Man Kwun; Korman, Matias et al.

28th International Symposium on Algorithms and Computation, ISAAC 2017. ed. / Takeshi Tokuyama; Yoshio Okamoto. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017. (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Banyassady, B, Chiu, MK, Korman, M, Mulzer, W, Van Renssen, A, Roeloffzen, M, Seiferth, P, Stein, Y, Vogtenhuber, B & Willert, M 2017, Routing in polygonal domains. in T Tokuyama & Y Okamoto (eds), 28th International Symposium on Algorithms and Computation, ISAAC 2017. Leibniz International Proceedings in Informatics, LIPIcs, vol. 92, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 28th International Symposium on Algorithms and Computation, ISAAC 2017, Phuket, Thailand, 17/12/9. https://doi.org/10.4230/LIPIcs.ISAAC.2017.10

Banyassady B, Chiu MK, Korman M, Mulzer W, Van Renssen A, Roeloffzen M et al. Routing in polygonal domains. In Tokuyama T, Okamoto Y, editors, 28th International Symposium on Algorithms and Computation, ISAAC 2017. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2017. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.ISAAC.2017.10

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title = "Routing in polygonal domains",

abstract = "We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of P, where each step must use only the label of the target node q and the routing table of the current node. For any fixed ϵ > 0, we present a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + ϵ. The labels have O(log n) bits, and the routing tables are of size O((ϵ-1+h) log n). The preprocessing time is O(n2 log n+hn2+ ϵ-1hn). It can be improved to O(n2 + ϵ-1n) for simple polygons.",

keywords = "Polygonal domains, Routing scheme, Small stretch, Yao graph",

author = "Bahareh Banyassady and Chiu, {Man Kwun} and Matias Korman and Wolfgang Mulzer and {Van Renssen}, Andr{\'e} and Marcel Roeloffzen and Paul Seiferth and Yannik Stein and Birgit Vogtenhuber and Max Willert",

note = "Funding Information: ∗ A full version of the paper is available at https://arxiv.org/abs/1703.09533. † BB was supported in part by DFG project MU/3501-2. ‡ MC was supported by JST ERATO Grant Number JPMJER1201, Japan. § MK was supported in part by KAKENHI Nos. 15H02665 and 17K12635, Japan. ¶ AvR was supported by JST ERATO Grant Number JPMJER1201, Japan. ‖ MR was supported by JST ERATO Grant Number JPMJER1201, Japan. ∗∗PS was supported in part by DFG project MU/3501-1. ††YS was supported by the DFG within the research training group {\textquoteleft}Methods for Discrete Structures{\textquoteright} (GRK 1408) and by GIF grant 1161.; 28th International Symposium on Algorithms and Computation, ISAAC 2017 ; Conference date: 09-12-2017 Through 22-12-2017",

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T1 - Routing in polygonal domains

AU - Banyassady, Bahareh

AU - Chiu, Man Kwun

AU - Korman, Matias

AU - Mulzer, Wolfgang

AU - Van Renssen, André

AU - Roeloffzen, Marcel

AU - Seiferth, Paul

AU - Stein, Yannik

AU - Vogtenhuber, Birgit

AU - Willert, Max

N1 - Funding Information: ∗ A full version of the paper is available at https://arxiv.org/abs/1703.09533. † BB was supported in part by DFG project MU/3501-2. ‡ MC was supported by JST ERATO Grant Number JPMJER1201, Japan. § MK was supported in part by KAKENHI Nos. 15H02665 and 17K12635, Japan. ¶ AvR was supported by JST ERATO Grant Number JPMJER1201, Japan. ‖ MR was supported by JST ERATO Grant Number JPMJER1201, Japan. ∗∗PS was supported in part by DFG project MU/3501-1. ††YS was supported by the DFG within the research training group ‘Methods for Discrete Structures’ (GRK 1408) and by GIF grant 1161.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of P, where each step must use only the label of the target node q and the routing table of the current node. For any fixed ϵ > 0, we present a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + ϵ. The labels have O(log n) bits, and the routing tables are of size O((ϵ-1+h) log n). The preprocessing time is O(n2 log n+hn2+ ϵ-1hn). It can be improved to O(n2 + ϵ-1n) for simple polygons.

AB - We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of P, where each step must use only the label of the target node q and the routing table of the current node. For any fixed ϵ > 0, we present a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + ϵ. The labels have O(log n) bits, and the routing tables are of size O((ϵ-1+h) log n). The preprocessing time is O(n2 log n+hn2+ ϵ-1hn). It can be improved to O(n2 + ϵ-1n) for simple polygons.

KW - Polygonal domains

KW - Routing scheme

KW - Small stretch

KW - Yao graph

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DO - 10.4230/LIPIcs.ISAAC.2017.10

M3 - Conference contribution

AN - SCOPUS:85038595037

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 28th International Symposium on Algorithms and Computation, ISAAC 2017

A2 - Tokuyama, Takeshi

A2 - Okamoto, Yoshio

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

T2 - 28th International Symposium on Algorithms and Computation, ISAAC 2017

Y2 - 9 December 2017 through 22 December 2017

ER -

Routing in polygonal domains

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