On routing with guaranteed delivery in three-dimensional ad hoc wireless networks

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. Sp...

• Type: Journal
• Year: 2010
• Where: WINET
• Authors: Stephane Durocher, David G. Kirkpatrick, Lata Narayanan
• Keywords: Algorithm, Routing Algorithm, Unit Ball, WINET 2010