# 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} }

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.

## 82 Citations

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- MathematicsESA
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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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- Computer Science, MathematicsESA
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This work presents a simple shortest path algorithm that runs in linear time if the input lengths are positive and uniformly distributed, and the worst-case running time is O(m + n log C).

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- Computer ScienceJACM
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A deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights, which avoids the sorting bottleneck by building a hierarchical bucketing structure.

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This paper gives simple label-setting and label-correcting algorithms for arbitrary directed graphs with random real edge weights uniformly distributed in [0; 1℄] and shows that they need linear timeO(n+m) with high probability.

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- Business, Computer Science2010 International Conference on Information and Emerging Technologies
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Initial finding and achievements to recover from a single link failure on the shortest path with optimal alternate path keeping the cost low are presented.

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- Computer ScienceProceedings 38th Annual Symposium on Foundations of Computer Science
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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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- Computer ScienceISAAC
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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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- Computer Science
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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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- Computer ScienceSIAM J. Comput.
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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.

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- Computer Science, Business2011 IEEE Symposium on Computers & Informatics
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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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