# A Distributed Algorithm for Minimum-Weight Spanning Trees

@article{Gallager1983ADA, title={A Distributed Algorithm for Minimum-Weight Spanning Trees}, author={Robert G. Gallager and Pierre A. Humblet and Philip M. Spira}, journal={ACM Trans. Program. Lang. Syst.}, year={1983}, volume={5}, pages={66-77} }

Abstract : A distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log of N to the base 2 + 2E and a message…

## 1,227 Citations

A Distributed Synchronous Algorithm for Minimum-Weight Spanning Trees

- Computer Science
- 2012

This paper presents a distributed synchronous algorithm for constructing the Minimum-Weight Spanning Tree (MST) in a connected undirected graph with distinct edge weights. Each node in the graph is…

A Distributed Algorithm for Minimum Weight Directed Spanning Trees

- Computer ScienceIEEE Trans. Commun.
- 1983

A distributed algorithm is presented for constructing minimum weight directed spanning trees (arborescences), each with a distinct root node, in a strongly connected directed graph, with time to completion O(|N|^{2}) .

Incremental Distributed Asynchronous Algorithm for Minimum Spanning Trees

- Computer ScienceComput. Networks ISDN Syst.
- 1993

A Distributed Spanning Tree Algorithm

- Computer ScienceWDAG
- 1987

A distributed algorithm for constructing a spanning tree for connected undirected graphs with maximal message size loglogN+log(maxid)+3, where maxid is the maximal processor identity.

Improving the Time Complexity of Message-Optimal Distributed Algorithms for Minimum-Weight Spanning Trees

- Computer ScienceSIAM J. Comput.
- 1990

A distributed algorithm is presented that constructs the minimum-weight spanning tree of an undirected connected graph with distinct node identities that has the same message complexity as the previously known algorithm due to Gallager, Humblet, and Spira.

An almost linear time and O(nlogn+e) Messages distributed algorithm for minimum-weight spanning trees

- Computer Science26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
- 1985

A distributed algorithm is presented that constructs the minimum-weight spanning tree of an undirected connected graph with distinct edge weights and distinct node identities with time complexity O(nG(n)+ time units, an improvement from Gallager's O(nlogn)+.

The Distributed Minimum Spanning Tree Problem

- Computer ScienceBull. EATCS
- 2018

This article summarizes the long line of research in designing efficient distributed algorithms and showing lower bounds for the distributed MST problem, including the most recent developments which have focused on algorithms that are simultaneously round- and message-optimal.

Distributed Graph Exploration

- Computer Science
- 1997

This article describes algorithms to compute spanning trees in an undirected network, that is, partition the set of edges into tree edges (these will be directed from parent to child) and non-tree…

A Simple Algorithm for Computing Minimum Spanning Trees in the Internet

- Computer ScienceInf. Sci.
- 1997

## References

SHOWING 1-10 OF 12 REFERENCES

A Distributed Algorithm for Minimum Weight Directed Spanning Trees

- Computer ScienceIEEE Trans. Commun.
- 1983

A distributed algorithm is presented for constructing minimum weight directed spanning trees (arborescences), each with a distinct root node, in a strongly connected directed graph, with time to completion O(|N|^{2}) .

An O(|E| log log |V|) Algorithm for Finding Minimum Spanning Trees

- Computer ScienceInf. Process. Lett.
- 1975

A note on two problems in connexion with graphs

- Mathematics, Computer ScienceNumerische Mathematik
- 1959

A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.

Shortest connection networks and some generalizations

- Mathematics
- 1957

The basic problem considered is that of interconnecting a given set of terminals with a shortest possible network of direct links. Simple and practical procedures are given for solving this problem…

On the shortest spanning subtree of a graph and the traveling salesman problem

- Mathematics
- 1956

7. A. Kurosh, Ringtheoretische Probleme die mit dem Burnsideschen Problem uber periodische Gruppen in Zussammenhang stehen, Bull. Acad. Sei. URSS, Ser. Math. vol. 5 (1941) pp. 233-240. 8. J.…

Communication Complexity of Distributed Minimum Spanning Tree Algorithms

- Computer ScienceBerkeley Workshop
- 1977

February ACM Transactions on Programming Languages and Systems

- February ACM Transactions on Programming Languages and Systems
- 1980

Combinatorial Optimization-Networks and Matroids

- 1976