Abstract. 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 ).
In REF it is shown that if each link has a weight known to its endpoints, then a minimum-weight spanning tree can be found in O(log log n) rounds.
Minimum-Weight Spanning Tree Construction in O(log log n) Communication Rounds
SIAM J. Comput
Mathematics Computer Science