MST construction in O (log log n ) communication rounds
Zvi Lotker, Elan Pavlov, Boaz Patt-Shamir, David Peleg · 2003
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 that constructs a minimum-weight spanning tree in O(log log n) communication rounds, where in each round any process can send a message to each other process. This result is the first to break the ω(log n) parallel time complexity barrier with small message sizes.