Polynomial Time Prioritized Multi-Criteria k-Shortest Paths and k-Disjoint All-Criteria-Shortest Paths
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The Shortest Path Problem, in real-life applications, has to deal with multiple criteria. Finding all Pareto-optimal solutions for the multi-criteria single-source single-destination shortest path problem with non-negative edge lengths might yield a solution with the exponential number of paths. In the first part of this paper, we study specific settings of the multi-criteria shortest path problem, which are based on prioritized multi-criteria and on k-shortest paths. In the second part, we show a polynomial-time algorithm that, given an undirected graph G and a pair of vertices (s,t), finds prioritized multi-criteria 2-disjoint (vertex/edge) shortest paths between s and t. In the third part of the paper, we introduce the k-disjoint all-criteria-shortest paths problem, which is solved in time O(min(k|E|, |E|^3/2)).
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