Recent results on the single-source shortest paths problem

@article{Raman1997RecentRO,
  title={Recent results on the single-source shortest paths problem},
  author={Rajeev Raman},
  journal={SIGACT News},
  year={1997},
  volume={28},
  pages={81-87}
}
  • R. Raman
  • Published 1 June 1997
  • Mathematics
  • SIGACT News
We summarize the currently best known theoretical results for the single-source shortest paths problem for directed graphs with non-negative edge weights. We also point out that a recent result due to Cherkassky, Goldberg and Silverstein (1996) leads to even better time bounds for this problem than claimed by the authors. 
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82 Citations
Highly Influential Citations
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82 Citations

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  • 2001
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Undirected single source shortest paths in linear time
  • M. Thorup
  • Computer Science
    Proceedings 38th Annual Symposium on Foundations of Computer Science
  • 1997
TLDR
A deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with integer weights, avoids the sorting bottle-neck by building a hierarchical bucketing structure, identifying vertex pairs that may be visited in any order.
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The algorithm takes the hierarchy-based approach invented by Thorup, and, if the ratio between the maximum and minimum edge lengths is bounded by n(log n)O(1), it can solve the single-source problem in O(m + n log log n) time.
A near linear shortest path algorithm for weighted undirected graphs
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