Oriented Spanners
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Given a point set P in the Euclidean plane and a parameter t, we define an oriented t-spanner as an oriented subgraph of the complete bi-directed graph such that for every pair of points, the shortest cycle in G through those points is at most a factor t longer than the shortest oriented cycle in the complete bi-directed graph. We investigate the problem of computing sparse graphs with small oriented dilation. As we can show that minimising oriented dilation for a given number of edges is NP-hard in the plane, we first consider one-dimensional point sets. While obtaining a 1-spanner in this setting is straightforward, already for five points such a spanner has no plane embedding with the leftmost and rightmost point on the outer face. This leads to restricting to oriented graphs with a one-page book embedding on the one-dimensional point set. For this case we present a dynamic program to compute the graph of minimum oriented dilation that runs in O(n8) time for n points, and a greedy algorithm that computes a 5-spanner in O(n log n) time. Expanding these results finally gives us a result for two-dimensional point sets: we prove that for convex point sets the greedy triangulation results in an oriented O(1)-spanner.
Original language | English |
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Title of host publication | 31st Annual European Symposium on Algorithms, ESA 2023 |
Editors | Inge Li Gortz, Martin Farach-Colton, Simon J. Puglisi, Grzegorz Herman |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Publication date | 2023 |
Pages | 1-16 |
Article number | 26 |
ISBN (Electronic) | 9783959772952 |
DOIs | |
Publication status | Published - 2023 |
Event | 31st Annual European Symposium on Algorithms, ESA 2023 - Amsterdam, Netherlands Duration: 4 Sep 2023 → 6 Sep 2023 |
Conference
Conference | 31st Annual European Symposium on Algorithms, ESA 2023 |
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Land | Netherlands |
By | Amsterdam |
Periode | 04/09/2023 → 06/09/2023 |
Series | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 274 |
ISSN | 1868-8969 |
Bibliographical note
Publisher Copyright:
© Kevin Buchin, Joachim Gudmundsson, Antonia Kalb, Aleksandr Popov, Carolin Rehs, André van Renssen, and Sampson Wong.
- computational geometry, greedy triangulation, oriented graph, spanner
Research areas
ID: 382560406