We consider in-network computation of an arbitrary function over an arbitrary
communication network. A network with capacity constraints on the links is
given. Some nodes in the network generate data, e.g., like sensor nodes in a
sensor network. An arbitrary function of this distributed data is to be
obtained at a terminal node. The structure of the function is described by a
given computation schema, which in turn is represented by a directed tree. We
design computing and communicating schemes to obtain the function at the
terminal at the maximum rate.
Timer-based mechanisms are often used to help a given (sink) node select the
best helper node among many available nodes. Specifically, a node transmits a
packet when its timer expires, and the timer value is a monotone non-increasing
function of its local suitability metric.