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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Publication statusPublished - Apr 2020


  • 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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