Distributed MST for constant diameter graphs

Zvi Lotker*, Boaz Patt-Shamir, David Peleg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper considers the problem of distributively constructing a minimum-weight spanning tree (MST) for graphs of constant diameter in the bounded-messages model, where each message can contain at most B bits for some parameter B. It is shown that the number of communication rounds necessary to compute an MST for graphs of diameter 4 or 3 can be as high as Ω(3√n/√B)and Ω(√4n/√B), respectively. The asymptotic lower bounds hold for randomized algorithms as well. On the other hand, we observe that O(log n) communication rounds always suffice to compute an MST deterministically for graphs with diameter 2, when B = O(log n). These results complement a previously known lower bound of Ω(√2n/B) for graphs of diameter Ω(log n).

Original languageEnglish
Pages (from-to)453-460
Number of pages8
JournalDistributed Computing
Issue number6
StatePublished - Jun 2006


  • Distributed algorithm
  • Minimum-weight spanning tree


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