Compact and Low Delay Routing Labeling Scheme for Unit Disk Graphs

  • Authors:

  • Chenyu Yan;Yang Xiang;Feodor F. Dragan

  • Affiliations:

  • Algorithmic Research Laboratory, Department of Computer Science, Kent State University, Kent, U.S.A.;Algorithmic Research Laboratory, Department of Computer Science, Kent State University, Kent, U.S.A.;Algorithmic Research Laboratory, Department of Computer Science, Kent State University, Kent, U.S.A.

  • Venue:
  • WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
  • Year:
  • 2009

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Abstract

In this paper, we propose a new compact and low delay routing labeling scheme for Unit Disk Graphs (UDGs) which often model wireless ad hoc networks. We show that one can assign each vertex of an n ---vertex UDG G a compact O (log2 n )-bit label such that, given the label of a source vertex and the label of a destination, it is possible to compute efficiently, based solely on these two labels, a neighbor of the source vertex that heads in the direction of the destination. We prove that this routing labeling scheme has a constant hop route-stretch (= hop delay ), i.e., for each two vertices x and y of G , it produces a routing path with h (x ,y ) hops (edges) such that h (x ,y ) ≤ 3·d G (x ,y ) + 12, where d G (x ,y ) is the hop distance between x and y in G . To the best of our knowledge, this is the first compact routing scheme for UDGs which not only guaranties delivery but has a low hop delay and polylog label size. Furthermore, our routing labeling scheme has a constant length route-stretch.