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.
