In this paper we consider the problem of load balancing over heterogeneous networks, i.e. networks whose nodes have different speeds. We assume that tasks are indivisible and with different weights. Our goal is that of minimizing the maximum execution time over nodes. We provide a gossip-based distributed algorithm whose convergence to a bounded set is guaranteed. We show that the convergence time of the proposed algorithm relies ultimately on the average meeting time between two agents performing a random walk on a graph.
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