Broadcast and minimum spanning tree with o(m) messages in the asynchronous CONGEST model - Mashreghi, Ali; King, Valerie (Distributed computing, 2021)
We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with o ( m ) bits of communication, in a sufficiently dense graph with n nodes and m edges. For decades, it was believed that Ω ( m ) bits of communication are required for any algorithm that constructs a broadcast tree. In 2015, King, Kutten and Thorup showed that in the KT1 model where nodes have initial knowledge of their neighbours’ identities it is possible to construct MST in O ~ ( n ) messages in the synchronous CONGEST model. In the CONGEST model messages are of size O ( log n ) . However, no algorithm with o ( m ) messages was known for the asynchronous case. Here, we provide an algorithm that uses O ( n 3 / 2 log 3 / 2 n ) messages to find MST in the asynchronous CONGEST model. Our algorithm is randomized Monte Carlo and outputs MST with high probability. We will provide an algorithm for computing a spanning tree with O ( n 3 / 2 log 3 / 2 n ) messages. Given a spanning tree, we can compute MST with O ~ ( n ) messages.