A note of an O(n3/logn) time algorithm for all pairs shortest paths

doi:10.1016/j.ipl.2007.08.015

Information Processing Letters

Volume 105, Issue 3, 31 January 2008, Pages 114-116

https://doi.org/10.1016/j.ipl.2007.08.015 Get rights and content

Abstract

We improve the all pairs shortest path algorithm given by Takaoka to time complexity $O (n^{3} / \log n)$ . Our improvement is achieved by using a smaller table and therefore saves time for the algorithm.

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Cited by (8)

An O(n3log⁡log⁡n/log2⁡n) time algorithm for all pairs shortest paths
2016, Journal of Discrete Algorithms
A fast algorithm to find all-pairs shortest paths in complex networks
2012, Procedia Computer Science
Finding shortest paths is a fundamental problem in graph theory, which has a large amount of applications in many areas like computer science, operations research, network routing and network analysis. Although many exact and approximate algorithms have been proposed, it is still a time-consuming task to calculate shortest paths for large-scale networks with tremendous volume of data available in recent years. In this paper, we find that the classic Dijkstra's algorithm can be improved by simple modification. We propose a fast algorithm which utilize the preiously-calculated results to accelerate the latter calculation. Simple optimization strategies are also proposed with consideration of characteristics of scale-free complex networks. Our experimental results show that the average running time of our algorithm is lower than the Dijkstra's algorithm by a factor relating to the connection probability in random networks of ER model. The performance of our algorithm is significantly better than the Dijkstra's algorithm in scale-free networks generated by the AB model. The results show that the time complexity is reduced to about O(n^2.4) in scalefree complex networks. When the optimization strategies are applied, the algorithm performance is further improved slightly in scale-free networks.
The Floyd-Warshall algorithm on graphs with negative cycles
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A valley-free shortest path algorithm and its application in detecting critical links among autonomous systems
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Computing all-pairs shortest paths by leveraging low treewidth
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^☆: Research supported in part by NSF grant 0310245.

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Abstract

References (16)

All pairs shortest distances for graphs with small integer length edges

Inform. Comput.

Improved algorithms for all pairs shortest paths

Inform. Process. Lett.

On the all-pairs-shortest-path problem in unweighted undirected graphs

J. Comput. Syst. Sci.

A new upper bound on the complexity of the all pairs shortest path problem

Inform. Process. Lett.

An $O (n^{3} \log \log n / \log n)$ time algorithm for the all-pairs shortest path problem

Inform. Process. Lett.

The Design and Analysis of Computer Algorithms

Data Structures and Algorithms

All-pairs shortest paths with real weights in $O (n^{3} / \log n)$ time

Cited by (8)

An O(n<sup>3</sup>log⁡log⁡n/log<sup>2</sup>⁡n) time algorithm for all pairs shortest paths

A fast algorithm to find all-pairs shortest paths in complex networks

The Floyd-Warshall algorithm on graphs with negative cycles

A valley-free shortest path algorithm and its application in detecting critical links among autonomous systems

An O(n <sup>3</sup> log log n/ log <sup>2</sup> n) time algorithm for all pairs shortest paths

Computing all-pairs shortest paths by leveraging low treewidth

A note of an O(n3/logn) time algorithm for all pairs shortest paths☆

Abstract

Inform. Comput.

Inform. Process. Lett.

J. Comput. Syst. Sci.

Inform. Process. Lett.

Inform. Process. Lett.

The Design and Analysis of Computer Algorithms

Data Structures and Algorithms

All-pairs shortest paths with real weights in O(n3/logn) time

A note of an $O (n^{3} / \log n)$ time algorithm for all pairs shortest paths☆

All-pairs shortest paths with real weights in $O (n^{3} / \log n)$ time