Broadcast and minimum spanning tree with o(m) messages in the asynchronous CONGEST model
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We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with o(m) bits of communication, in a 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 neighbors' identities it is possible to construct MST in Õ(n) messages in the synchronous CONGEST model. In the CONGEST model messages are of size O( n). However, no algorithm with o(m) messages were known for the asynchronous case. Here, we provide an algorithm that uses O(n^3/2^3/2 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^3/2^3/2 n) messages. Given a spanning tree, we can compute MST with Õ(n) messages.
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