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On Routing with Guaranteed Delivery in Three-Dimensional Ad Hoc Wireless Networks

  • Stephane Durocher
  • David Kirkpatrick
  • Lata Narayanan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4904)

Abstract

We study routing algorithms for three-dimensional ad hoc networks that guarantee delivery and are k-local, i.e., each intermediate node v’s routing decision only depends on knowledge of the labels of the source and destination nodes, of the subgraph induced by nodes within distance k of v, and of the neighbour of v from which the message was received. We model a three-dimensional ad hoc network by a unit ball graph, where nodes are points in ℝ3, and nodes u and v are joined by an edge if and only if the distance between u and v is at most one.

The question of whether there is a simple local routing algorithm that guarantees delivery in unit ball graphs has been open for some time. In this paper, we answer this question in the negative: we show that for any fixed k, there can be no k-local routing algorithm that guarantees delivery on all unit ball graphs. This result is in contrast with the two-dimensional case, where 1-local routing algorithms that guarantee delivery are known. Specifically, we show that guaranteed delivery is possible if the nodes of the unit ball graph are contained in a slab of thickness \(1/\sqrt{2}\). However, there is no k-local routing algorithm that guarantees delivery for the class of unit ball graphs contained in thicker slabs, i.e., slabs of thickness \(1/\sqrt{2} + \epsilon\) for some ε> 0. The algorithm for routing in thin slabs derives from a transformation of unit ball graphs contained in thin slabs into quasi unit disc graphs, which yields a 2-local routing algorithm. We also show several results that further elaborate on the relationship between these two classes of graphs.

Keywords

Destination Node Label Graph Correspondent Node Geometric Graph Thin Slab 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Stephane Durocher
    • 1
  • David Kirkpatrick
    • 2
  • Lata Narayanan
    • 3
  1. 1.School of Computer ScienceMcGill UniversityCanada
  2. 2.Department of Computer ScienceUniversity of British ColumbiaCanada
  3. 3.Department of Computer ScienceConcordia UniversityCanada

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