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 eps > 0, we pre ent a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + eps. The labels have O(log n) bits, and the routing tables are of size O((eps^{-1} + h) log n). The preprocessing time is O(n^2 log n + hn^2 + eps^{-1}hn). It can be improved to O(n 2 + eps^{-1}n) for simple polygons.
@InProceedings{banyassady_et_al:LIPIcs.ISAAC.2017.10, author = {Banyassady, Bahareh and Chiu, Man-Kwun and Korman, Matias and Mulzer, Wolfgang and van Renssen, Andr\'{e} and Roeloffzen, Marcel and Seiferth, Paul and Stein, Yannik and Vogtenhuber, Birgit and Willert, Max}, title = {{Routing in Polygonal Domains}}, booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)}, pages = {10:1--10:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-054-5}, ISSN = {1868-8969}, year = {2017}, volume = {92}, editor = {Okamoto, Yoshio and Tokuyama, Takeshi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.10}, URN = {urn:nbn:de:0030-drops-82379}, doi = {10.4230/LIPIcs.ISAAC.2017.10}, annote = {Keywords: polygonal domains, routing scheme, small stretch,Yao graph} }
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