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Issue No. 09 - September (2010 vol. 59)
ISSN: 0018-9340
pp: 1224-1238
Hannes Frey , University of Paderborn, Paderborn, Germany
Ivan Stojmenovic , University of Ottawa, Ontario, Canada
In this paper, we provide a thorough theoretical study on delivery guarantees, loop-free operation, and worst-case behavior of face and combined greedy-face routing. We show that under specific planar topology control schemes, recovery from a greedy routing failure is always possible without changing between any adjacent faces. Guaranteed delivery then follows from guaranteed recovery while traversing the very first face. In arbitrary planar graphs, however, a proper face selection mechanism is of importance since recovery from a greedy routing failure may require visiting a sequence of faces before greedy routing can be restarted again. We provide complete and formal proofs that several proposed face routing and combined greedy-face routing schemes guarantee message delivery in specific planar graph classes or even in arbitrary planar graphs. We also discuss the reasons why other methods fail to deliver a message or even end up in a loop. In addition, we investigate the behavior of face routing in arbitrary not necessarily planar networks and show, while delivery guarantees cannot be supported in such a general case, most face and combined greedy-face routing variants support at least loop-free operation. For those variants, we derive worst-case upper bounds on the number of forwarding steps.
Ad hoc network, sensor network, face routing, correctness analysis, worst-case analysis.

I. Stojmenovic and H. Frey, "On Delivery Guarantees and Worst-Case Forwarding Bounds of Elementary Face Routing Components in Ad Hoc and Sensor Networks," in IEEE Transactions on Computers, vol. 59, no. , pp. 1224-1238, 2010.
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