Distributed verification of minimum spanning trees

Amos Korman, Shay Kutten

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The problem of verifying a Minimum Spanning Tree (MST) was introduced by Tarjan in a sequential setting. Given a graph and a tree that spans it, the algorithm is required to check whether this tree is an MST. This paper investigates the problem in the distributed setting, where the input is given in a distributed manner, i.e., every node "knows" which of its own emanating edges belong to the tree. Informally, the distributed MST verification problem is the following. Label the vertices of the graph in such a way that for every node, given its own label and the labels of its neighbors only, the node can detect whether these edges are indeed its MST edges. In this paper we present such a verification scheme with a maximum label size of O(log n log W), where n is the number of nodes and W is the largest weight of an edge. We also give a matching lower bound of Ω(log n log W) (except when W ≤ log n). Both our bounds improve previously known bounds for the problem. For the related problem of tree sensitivity also presented by Tarjan, our method yields rather efficient schemes for both the distributed and the sequential settings. Our techniques (both for the lower bound and for the upper bound) may indicate a strong relation between the fields of proof labeling schemes and implicit labeling schemes.

Original languageEnglish
Title of host publicationProceedings of the 25th Annual ACM Symposium on Principles of Distributed Computing 2006
PublisherAssociation for Computing Machinery (ACM)
Number of pages9
ISBN (Print)1595933840, 9781595933843
StatePublished - 2006
Externally publishedYes
Event25th Annual ACM Symposium on Principles of Distributed Computing 2006 - Denver, CO, United States
Duration: 23 Jul 200626 Jul 2006

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference25th Annual ACM Symposium on Principles of Distributed Computing 2006
Country/TerritoryUnited States
CityDenver, CO


  • Distributed algorithms
  • Graph property verification
  • Labeling schemes
  • Minimum Spanning Tree
  • Network algorithms
  • Proof labeling
  • Self stabilization

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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