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We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits. For this model, we present a distributed algorithm which constructs a minimum-weight spanning tree in O(log log n) communication rounds, where in each round any process can send a message to every other process. If message size is Θ(n ) for some > 0, then the number of communication rounds is O(log 1 ).doi:10.1137/s0097539704441848 fatcat:e5nknu7onnhqlenfmyqz33mvmm