Minimum-Weight Spanning Tree Construction in O(log log n) Communication Rounds

Authors:
Zvi Lotker;Boaz Patt-Shamir;Elan Pavlov;David Peleg
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Computing
Year:
2005

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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 $\Theta(n^\epsilon)$ for some $\epsilon0$, then the number of communication rounds is $O(\log{1\over\epsilon})$.