An Application of an Initialization Protocol to Permutation Routing in a Single-Hop Mobile Ad Hoc Networks

Abstract

In 1999 Nakano, Olariu, and Schwing in [20], they showed that the permutation routing of n items pretitled on a mobile ad hoc network (MANET for short) of p stations (p known) and k channels (MANET{(n, p, k)) with k < p, can be carried out in $\frac{2n}{k} + k - 1$ broadcast rounds if k ≤ √p and if each station has a $O(\frac{n}{k})$-memory locations. And if k ≤ $\smash{\sqrt{\frac {p} {2}}}$ and if each station has a $O(\frac{n}{p})$-memory locations, the permutations of these n pretitled items can be done also in $\smash{\frac{2n}{k} + k - 1}$ broadcast rounds. They used two assumptions: first they suppose that each station of the mobile ad hoc network has an identifier beforehand. Secondly, the stations are partitioned into k groups such that each group has $\frac{p}{k}$ stations, but it was not shown how this partition can be obtained. In this paper, the stations have not identifiers beforehand and p is unknown. We develop a protocol which first names the stations, secondly gives the value of p, and partitions stations in groups of $\frac{p}{k}$ stations. Finally we show that the permutation routing problem can be solved on it in $O (\frac{p}{\ln2}) + (\frac{2}{k} + 1)n + k - 1$ broadcast rounds in the worst case. It can be solved in $O(\frac{p}{\ln2})+(\frac{2}{k})n+k-1$ broadcast rounds in the better case. Note that our approach does not impose any restriction on k.