# Undirected single-source shortest paths with positive integer weights in linear time

@article{Thorup1999UndirectedSS, title={Undirected single-source shortest paths with positive integer weights in linear time}, author={M. Thorup}, journal={J. ACM}, year={1999}, volume={46}, pages={362-394} }

The single-source shortest paths problem (SSSP) is one of the classic problems in algorithmic graph theory: given a positively weighted graph G with a source vertex s, find the shortest path from s to all other vertices in the graph.
Since 1959, all theoretical developments in SSSP for general directed and undirected graphs have been based on Dijkstra's algorithm, visiting the vertices in order of increasing distance from s. Thus, any implementation of Dijkstra's algorithm sorts the verticesâ€¦Â CONTINUE READING

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#### References

SHOWING 1-4 OF 4 REFERENCES

A scaling algorithm for weighted matching on general graphs

- Mathematics, Computer Science
- 26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
- 1985

112 Highly Influential

Trans-dichotomous algorithms for minimum spanning trees and shortest paths

- Computer Science
- Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science
- 1990

215 Highly Influential- PDF

Trans-dichotomous algorithms for minimum

- 1994

A linear-time algorithm for a special case

- 1985