  The work here studies the communication cost for a multi-server multi-task
distributed computation framework, and does so for a broad class of functions
and data statistics. Considering the framework where a user seeks the
computation of multiple complex (conceivably non-linear) tasks from a set of
distributed servers, we establish communication cost upper bounds for a variety
of data statistics, function classes and data placements across the servers. To
do so, we proceed to apply, for the first time here, K\"orner's characteristic
graph approach -- which is known to capture the structural properties of data
and functions -- to the promising framework of multi-server multi-task
distributed computing. Going beyond the general expressions, and in order to
offer clearer insight, we also consider the well-known scenario of cyclic
dataset placement and linearly separable functions over the binary field, in
which case our approach exhibits considerable gains over the state of art.
Similar gains are identified for the case of multi-linear functions.
