2022/10/06 by Peter M. Robinson, Robinson, Peter
Computer Science · #Complexity and Algorithms in Graphs #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #Distributed #FOS: Computer and information sciences #Machine Learning and Algorithms #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2210.02638
openalex publication_date 2022/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that any one-round algorithm that computes a minimum spanning tree (MST) in the unicast congested clique must use a link bandwidth of Ω(log3 n) bits in the worst case. Consequently, computing an MST under the standard assumption of O(log n)-size messages requires at least 2 rounds. This is the first round complexity lower bound in the unicast congested clique for a problem where the output size is small, i.e., O(nlog n) bits. Our lower bound holds as long as every edge of the MST is output by an incident node. To the best of our knowledge, all prior lower bounds for the unicast congested clique either considered problems with large output sizes (e.g., triangle enumeration) or required every node to learn the entire output.