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. 
Exact and Approximate Distances in Graphs - A Survey
We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different
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Directed single-source shortest-paths in linear average-case time
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  • Computer Science, Mathematics
  • 2001
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TLDR
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  • 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 experimental results suggest that the caliber heuristic and adaptive parameter selection give an efficient algorithm, both on typical and on hard inputs, for a wide range of arc lengths.
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It is demonstrated that the proposed new single-source shortest path algorithm for nonnegative weight graph is faster than Dijkstra's algorithm using Fibonacci heap in average situation when n is large enough.
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TLDR
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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The presented algorithm uses Depth First Search like graph traversal during a BFS like traversal i.e. combines and take advantage of the inherent properties of the two heuristic graph search techniques so that vertex weights can be kept balanced.
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