# Shortest connection networks and some generalizations

@article{Prim1957ShortestCN, title={Shortest connection networks and some generalizations}, author={Robert C. Prim}, journal={Bell System Technical Journal}, year={1957}, volume={36}, pages={1389-1401} }

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 both graphically and computationally. It develops that these procedures also provide solutions for a much broader class of problems, containing other examples of practical interest.

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## References

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.…