### Energy-optimal algorithms for computing aggregative functions in random networks

*Marek Klonowski, Malgorzata Sulkowska*

#### Abstract

We investigate a family of algorithms minimizing energetic effort in
random networks computing aggregative functions. In contrast to
previously considered models, our results minimize maximal energetic
effort over all stations instead of the average usage of energy. Such
approach seems to be much more suitable for some kinds of networks, in
particular ad hoc radio networks, wherein we need all stations
functioning and replacing batteries after the deployment is not
feasible. We analyze also the latency of proposed energy-optimal
algorithms. We model a network by placing randomly and independently
n points in a d-dimensional cube of
side-length n

^{1/d}. We place an edge between vertices that interact with each other. We analyze properties of the resulting graphs in order to obtain estimates on energetic effort and latency of proposed algorithms.Full Text: PDF