  In this paper, we consider a class of workspace partitioning problems that
arise in the context of area coverage and spatial load balancing for spatially
distributed heterogeneous multi-agent networks. It is assumed that each agent
has certain directions of motion or directions for sensing and exploration that
are more preferable than others. These preferences are measured by means of
convex and anisotropic (direction-dependent) quadratic proximity metrics which
are, in general, different for each agent. These proximity metrics induce
Voronoi-like partitions of the network's workspace that are comprised of cells
which may not always be convex (or even connected) sets but are necessarily
contained in ellipsoids that are known to their corresponding agents. The main
contributions of this work are 1) a distributed algorithm for the computation
of a Voronoi-like partition of the workspace of a heterogeneous multi-agent
network and 2) a systematic process to discover the network topology induced by
the latter Voronoi-like partition. Numerical simulations that illustrate the
efficacy of the proposed algorithms are also presented.
