Node ID assignment in group theoretic graphs for WSNs

In this paper, we investigate and present different node ID assignment algorithms for group-theoretic graphs such as Borel Cayley and de Bruijn graphs. These graphs have been shown to be effective logical topologies in wireless sensor networks when all the nodes are within communication range of each other. However, in practice a sensor node's communication range is limited and some nodes can be out of range with each other. Under this more realistic scenario, the original theoretic graph cannot be imposed to the network in its entirety. But rather, only partial connections of the original graphs can be imposed on the physical network. Thus, node ID assignment becomes an important issue. An effective assignment allows most connections to be imposed and hence resulting in a shorter diameter and the average path length. We investigate three algorithms: (a) ID swapping assignment, (b) simulated annealing based assignment, and (c) distributed ID swapping assignment. While the first two are centralized algorithms that are appropriate for wireless sensor network with fixed infrastructure, the latter is efficient for ad hoc WSNs. As expected, being most computationally intensive, simulated annealing has the best performance, and all three methods outperforms random ID assignment for our simulations.