  The paper deals with the distributed minimum sharing problem: a set of
decision-makers compute the minimum of some local quantities of interest in a
distributed and decentralized way by exchanging information through a
communication network. We propose an adjustable approximate solution which
enjoys several properties of crucial importance in applications. In particular,
the proposed solution has good decentralization properties and it is scalable
in that the number of local variables does not grow with the size or topology
of the communication network. Moreover, a global and uniform (both in the
initial time and in the initial conditions) asymptotic stability result is
provided towards a steady state which can be made arbitrarily close to the
sought minimum. Exact asymptotic convergence can be recovered at the price of
losing uniformity with respect to the initial time.
