Solving k-shortest and constrained shortest path problems efficiently
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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+Knlog(m/n)) time. Experimental results presented in this paper show that the algorithm outperforms in practice the algorithms by Eppstein [7,8] and by Martins and Santos [15] for different kinds of random generated graphs.