In this paper we present AFR, a new geometric mobile adhoc routing algorithm. The algorithm is completely distributed; nodes need to communicate only with direct neighbors in their transmission range. We show that if a best route has cost c, AFR finds a route and terminates with cost O(c 2 ) in the worst case. AFR is the first algorithm with cost bounded by a function of the optimal route. We also give a tight lower bound by showing that any geometric routing algorithm has worst-case cost Ω(c 2 ). Thus AFR is asymptotically optimal. We give a non-geometric algorithm that also matches the lower bound, but needs some memory at each node. This establishes an intriguing trade-off between geometry and memory.
The first algorithm that gives worst case guarantees is by Kuhn et al. REF .
Asymptotically optimal geometric mobile ad-hoc routing
DIALM '02
Computer Science Mathematics