  As is well known, energy cost can greatly impact the deployment of
battery-powered sensor networks in remote environments such as rivers or
oceans. Motivated by this, we propose here an energy-based metric and associate
energy-based Voronoi partitions with mobile vehicles in constant flows. The
metric corresponds to the minimum energy that a vehicle requires to move from
one point to another in the flow environment, and the resulting partition can
be used by the vehicles in cooperative control tasks such as task assignment
and coverage. Based on disk-based and asymptote-based approximations of the
Voronoi regions, we determine a subset (or lower bound) and superset (or upper
bound) of an agent's Voronoi neighbors. We then show that, via simulations, the
upper bound is tight and its cardinality remains bounded as the number of
generators increases. Finally, we propose efficient algorithms to compute the
upper bound (especially when the generators dynamically change), which enables
the fast calculation of Voronoi regions.
