Computing the K Shortest Paths: A New Algorithm and an Experimental Comparison
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- Jiménez V.M., Marzal A. (1999) Computing the K Shortest Paths: A New Algorithm and an Experimental Comparison. In: Vitter J.S., Zaroliagis C.D. (eds) Algorithm Engineering. WAE 1999. Lecture Notes in Computer Science, vol 1668. Springer, Berlin, Heidelberg
A new algorithm to compute the K shortest paths (in order of increasing length) between a given pair of nodes in a digraph with n nodes and m arcs is presented. The algorithm recursively and efficiently solves a set of equations which generalize the Bellman equations for the (single) shortest path problem and allows a straightforward implementation. After the shortest path from the initial node to every other node has been computed, the algorithm finds the K shortest paths in O(m+ Kn log(m/n)) time. Experimental results presented in this paper show that the algorithm outperforms in practice the algorithms by Eppstein , and by Martins and Santos  for different kinds of random generated graphs.
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