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

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

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 $varepsilon > 0$, we present a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most $1 + . The labels have $O(log n)$ bits, and the routing tables are of size $O((-1+h)log n)$. The preprocessing time is $O(n^2log n + hn^2+-1hn)$. It can be improved to $O(n^2+-1n)$ for simple polygons.
Original languageEnglish
Title of host publication28th International Symposium on Algorithms and Computation (ISAAC 2017)
EditorsYoshio Okamoto, Takeshi Tokuyama
Place of PublicationDagstuhl, Germany
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Pages10:1-10:13
Volume92
ISBN (Print)978-3-95977-054-5
DOIs
Publication statusPublished - 2017

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik

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Banyassady, B., Chiu, M-K., Korman, M., Mulzer, W., Renssen, A. V., Roeloffzen, M., ... Willert, M. (2017). Routing in Polygonal Domains. In Y. Okamoto, & T. Tokuyama (Eds.), 28th International Symposium on Algorithms and Computation (ISAAC 2017) (Vol. 92, pp. 10:1-10:13). (Leibniz International Proceedings in Informatics (LIPIcs)). Dagstuhl, Germany: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.ISAAC.2017.10

Routing in Polygonal Domains. / Banyassady, Bahareh; Chiu, Man-Kwun; Korman, Matias; Mulzer, Wolfgang; Renssen, André van; Roeloffzen, Marcel; Seiferth, Paul; Stein, Yannik; Vogtenhuber, Birgit; Willert, Max.

28th International Symposium on Algorithms and Computation (ISAAC 2017). ed. / Yoshio Okamoto; Takeshi Tokuyama. Vol. 92 Dagstuhl, Germany : Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2017. p. 10:1-10:13 (Leibniz International Proceedings in Informatics (LIPIcs)).

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

Banyassady, B, Chiu, M-K, Korman, M, Mulzer, W, Renssen, AV, Roeloffzen, M, Seiferth, P, Stein, Y, Vogtenhuber, B & Willert, M 2017, Routing in Polygonal Domains. in Y Okamoto & T Tokuyama (eds), 28th International Symposium on Algorithms and Computation (ISAAC 2017). vol. 92, Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, pp. 10:1-10:13. https://doi.org/10.4230/LIPIcs.ISAAC.2017.10
Banyassady B, Chiu M-K, Korman M, Mulzer W, Renssen AV, Roeloffzen M et al. Routing in Polygonal Domains. In Okamoto Y, Tokuyama T, editors, 28th International Symposium on Algorithms and Computation (ISAAC 2017). Vol. 92. Dagstuhl, Germany: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik. 2017. p. 10:1-10:13. (Leibniz International Proceedings in Informatics (LIPIcs)). https://doi.org/10.4230/LIPIcs.ISAAC.2017.10
Banyassady, Bahareh ; Chiu, Man-Kwun ; Korman, Matias ; Mulzer, Wolfgang ; Renssen, André van ; Roeloffzen, Marcel ; Seiferth, Paul ; Stein, Yannik ; Vogtenhuber, Birgit ; Willert, Max. / Routing in Polygonal Domains. 28th International Symposium on Algorithms and Computation (ISAAC 2017). editor / Yoshio Okamoto ; Takeshi Tokuyama. Vol. 92 Dagstuhl, Germany : Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2017. pp. 10:1-10:13 (Leibniz International Proceedings in Informatics (LIPIcs)).
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AU - Korman, Matias

AU - Mulzer, Wolfgang

AU - Renssen, André van

AU - Roeloffzen, Marcel

AU - Seiferth, Paul

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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 $varepsilon > 0$, we present a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most $1 + . The labels have $O(log n)$ bits, and the routing tables are of size $O((-1+h)log n)$. The preprocessing time is $O(n^2log n + hn^2+-1hn)$. It can be improved to $O(n^2+-1n)$ 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 $varepsilon > 0$, we present a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most $1 + . The labels have $O(log n)$ bits, and the routing tables are of size $O((-1+h)log n)$. The preprocessing time is $O(n^2log n + hn^2+-1hn)$. It can be improved to $O(n^2+-1n)$ for simple polygons.

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