# On the History of the Minimum Spanning Tree Problem

@article{Graham1985OnTH, title={On the History of the Minimum Spanning Tree Problem}, author={Ronald L. Graham and Pavol Hell}, journal={Annals of the History of Computing}, year={1985}, volume={7}, pages={43-57} }

It is standard practice among authors discussing the minimum spanning tree problem to refer to the work of Kruskal(1956) and Prim (1957) as the sources of the problem and its first efficient solutions, despite the citation by both of Boruvka (1926) as a predecessor. In fact, there are several apparently independent sources and algorithmic solutions of the problem. They have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century. We shall explore and compare…

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## References

SHOWING 1-10 OF 121 REFERENCES

### On Finding and Updating Spanning Trees and Shortest Paths

- Computer Science, MathematicsSIAM J. Comput.
- 1975

The most notable result is that a spanning tree solution can be updated in $O(n)$ when a new node is added to an n-node graph whose minimum spanning tree is known.

### Computing capacitated minimal spanning trees efficiently

- Computer ScienceNetworks
- 1974

An analysis is made of the computational complexity of a class of heuristic algorithms for the solution of the minimal spanning tree problem subject to a restriction on the maximum number (or weight)…

### Finding Minimum Spanning Trees

- Mathematics, Computer ScienceSIAM J. Comput.
- 1976

This paper studies methods for finding minimum spanning trees in graphs and results include relationships with other problems which might lead general lower bound for the complexity of the minimum spanning tree problem.

### Finding Minimum Spanning Trees with a Fixed Number of Links at a Node

- Computer Science
- 1975

This paper addresses a variant of the minimum spanning tree problem in which a given node is required to have a fixed number of incident edges and shows that this problem can be solved by a highly efficient “quasi-greedy” algorithm.

### 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.…

### Computing minimum spanning trees efficiently

- Computer ScienceACM Annual Conference
- 1972

Modifications to both Prim's and Kruskal's Algorithms are introduced which give significant improvements for the complete range of sparseness, and a dramatic reduction in execution time can be obtained for sparse networks when the network under consideration is sparse.

### Two Algorithms for Generating Weighted Spanning Trees in Order

- Computer ScienceSIAM J. Comput.
- 1977

Two algorithms for generating spanning trees of a connected graph in order of increasing weight are presented. The first generates the K smallest weight trees, where K can be specified in advance or…

### Improvements of the Held—Karp algorithm for the symmetric traveling-salesman problem

- Computer ScienceMath. Program.
- 1974

A highly efficient algorithm (HK) devised by Held and Karp for solving the symmetric traveling-salesman problem was presented at the 7th Mathematical Programming Symposium in 1970 and published in…