An All Pairs Shortest Path Algorithm with Expected Time $O(n^2 \log n)$

1987 ◽  
Vol 16 (6) ◽  
pp. 1023-1031 ◽  
Author(s):  
Alistair Moffat ◽  
Tadao Takaoka
Keyword(s):  
Shortest Path ◽  
Shortest Path Algorithm ◽  
Expected Time ◽  
All Pairs Shortest Path

Research and development of Johnson's algorithm parallel schemes in GPGPU technology

2016 ◽  
pp. 105-112
Author(s):  
S.D. Pogorilyy ◽  
◽  
M.S. Slynko ◽  
Keyword(s):  
Experimental Study ◽  
Research And Development ◽  
Shortest Path ◽  
Shortest Path Algorithm ◽  
Suggested Approach ◽  
Nvidia Cuda ◽  
Weighted Directed Graph ◽  
Improved Performance ◽  
Systems Of Algorithmic Algebras ◽  
All Pairs Shortest Path

Johnson’s all pairs shortest path algorithm application in an edge weighted, directed graph is considered. Its formalization in terms of Glushkov’s modified systems of algorithmic algebras was made. The expediency of using GPGPU technology to accelerate the algorithm is proved. A number of schemas of parallel algorithm optimized for using in GPGPU were obtained. Suggested approach to the implementation of the schemes obtained using computing architecture NVIDIA CUDA. An experimental study of improved performance by using GPU for computations was made.

scholarly journals An all-pairs shortest path algorithm for bipartite graphs

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Svetlana Torgasin ◽  
Karl-Heinz Zimmermann
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Shortest Paths ◽  
Distance Matrix ◽  
Bipartite Graphs ◽  
Matrix Product ◽  
Complex Structures ◽  
Shortest Path Algorithm ◽  
Order Of Magnitude ◽  
All Pairs Shortest Path

AbstractBipartite graphs are widely used for modeling of complex structures in biology, engineering, and computer science. The search for shortest paths in such structures is a highly demanded procedure that requires optimization. This paper presents a variant of the all-pairs shortest path algorithm for bipartite graphs. The method is based on the distance matrix product and improves the general algorithm by exploiting the graph topology. The space complexity is reduced by a factor of at least four and the time complexity decreased by almost an order of magnitude when compared with the basic APSP algorithm.

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