We introduce hierarchical neighbor graphs, a new architecture for connecting ad hoc wireless nodes distributed in a plane. The structure has the flavor of hierarchical clustering and requires only local knowledge and minimal computation at each node to be formed and repaired. Hence, it is a suitable interconnection model for an ad hoc wireless sensor network. The structure is able to use energy efficiently by reorganizing dynamically when the battery power of heavily utilized nodes degrades and is able to achieve throughput, energy efficiency and network lifetimes that compare favorably with the leading proposals for data collation in sensor networks such as LEACH (Heinzelman et. al., 2002). Additionally, hierarchical neighbor graphs have low power stretch i.e. the power required to connect nodes through the network is a small factor higher than the power required to connect them directly. Our structure also compares favorably to mathematical structures proposed for connecting points in a plane e.g. nearest-neighbor graphs (Ballister et. al., 2005), @math -graphs (Ruppert and Seidel, 1991), in that it has expected constant degree and does not require any significant computation or global information to be formed.
Skip lists are data structures that use probabilistic balancing rather than strictly enforced balancing. As a result, the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees. We design a variation of skip lists that performs well for generally biased access sequences. Given n items, each with a positive weight wi, 1 ≤ i ≤ n, the time to access item i is O(1 + log (W wi)), where W=∑i=1nwi; the data structure is dynamic. We present two instantiations of biased skip lists, one of which achieves this bound in the worst case, the other in the expected case. The structures are nearly identical; the deterministic one simply ensures the balance condition that the randomized one achieves probabilistically. We use the same method to analyze both.