| D. R. Shier: "On Algorithms for Finding the k Shortest Paths in a Network", Networks, vol. 9, pp. 195--214. (1979) |
.... log d) where d is the maximum input degree [Fox73, Fox78] This algorithm computes the K shortest paths from s to all the nodes in V (even if we are interested only in the K shortest paths from s to t) Therefore, its best case time complexity is Omega Gamma A K Delta jV j) Shier proposed in [Shie76, Shie79] several methods for the computation of the K shortest paths. In practice, the so called Label Setting algorithm was shown to be the most efficient one. It can be seen as a generalization of Dijkstra s shortest path algorithm and works only in graphs with nonnegative arcs. The time complexity of ....
D. R. Shier: "On Algorithms for Finding the k Shortest Paths in a Network", Networks, vol. 9, pp. 195--214. (1979)
....indicated when (1) the edges of the network have non negative costs and (2) the shortest paths from a central vertex to all other vertices must be computed. Furthermore, networks found in telecommunications applications are sparse and label setting algorithms are particularly e#cient in this case [28]. In this adaptation, the scalar label associated with every vertex i is replaced by a vector # i of size k whose p th element # p i is an upper bound on the length of the p th shortest path to vertex i (i.e. the labels are sorted in nondecreasing order) 23] Two pointers are also associated ....
Shier D.R. (1979), "On Algorithms for Finding the k-Shortest Paths in a Network", Networks 9, 195--214.
....pair of nodes in the network. B. Solution Approach The problem now has been reduced to finding the k shortest paths between every pair of nodes in the satellite network. The strategy adopted to obtain the required switching tables is given below: 1) Solutions to the k shortest path problem [4,8,15, 18] are used to calculate k number of shortest paths for each source destination pair for each snapshot, where 1 k n (n = number of satellites in the network) 2) The data stream is routed along the k th shortest path based on the latency and bandwidth requirements. Thus, real time data may be ....
Douglas R. Shier, "On Algorithms for Finding the k Shortest Paths in a Network", Networks Journal, Vol.9, No.3, 1979.
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