Tight Bounds for Distributed Minimum-Weight Spanning Tree Verification
This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities of this problem. Specifically, we provide an MST verification algorithm that achieves simultaneously \(\tilde{O}(m)\) messages and \(\tilde{O}(\sqrt{n} + D)\) time, where m is the number of edges in the given graph G, n is the number of nodes, and D is Gs diameter. On the other hand, we show that any MST verification algorithm must send \(\tilde{\varOmega}(m)\) messages and incur \(\tilde{\varOmega}(\sqrt{n} + D)\) time in worst case.
minimum-weight spanning tree distributed verification distributed algorithms labeling schemes