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: Contribution to journalArticle

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 of P. 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 whose length 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(n2log⁡n). It can be improved to O(n2) for simple polygons.

Original languageEnglish
Article number101593
JournalComputational Geometry: Theory and Applications
Volume87
DOIs
Publication statusPublished - 2020 Apr

Keywords

  • Polygonal domain
  • Routing scheme

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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  • Cite this

    Banyassady, B., Chiu, M. K., Korman, M., Mulzer, W., van Renssen, A., Roeloffzen, M., Seiferth, P., Stein, Y., Vogtenhuber, B., & Willert, M. (2020). Routing in polygonal domains. Computational Geometry: Theory and Applications, 87, [101593]. https://doi.org/10.1016/j.comgeo.2019.101593