Fast discrete consensus based on gossip for makespan minimization in networked systems

In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm optimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art and grows at worst quadratically with respect to the number of nodes.