Data structures and network algorithms
Data structures and network algorithms
A linear algorithm for finding dominators in flow graphs and related problems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
Crash failures can drive protocols to arbitrary states
PODC '96 Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing
The complexity of crash failures
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
An optimal EREW PRAM algorithm for minimum spanning tree verification
Information Processing Letters
The local detection paradigm and its applications to self-stabilization
Theoretical Computer Science
Fast distributed construction of small k-dominating sets and applications
Journal of Algorithms
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
A Distributed Algorithm for Minimum-Weight Spanning Trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Labeling schemes for flow and connectivity
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Constant-time distributed dominating set approximation
Distributed Computing
Local MST computation with short advice
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Controller and estimator for dynamic networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Online Computation with Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Online computation with advice
Theoretical Computer Science
Distributed decision problems: the locality angle
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Distributed verification and hardness of distributed approximation
Proceedings of the forty-third annual ACM symposium on Theory of computing
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Memory lower bounds for randomized collaborative search and implications for biology
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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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.