An algorithm builds a data structure for all distinct parametric shortest paths in a linearly interpolated graph in Θ(k|E| log |V|) time, supporting Θ(log k) queries where k counts the distinct paths that are shortest over nontrivial intervals.
Karp and James B
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Parametric Shortest Paths in a Linearly Interpolated Graph
An algorithm builds a data structure for all distinct parametric shortest paths in a linearly interpolated graph in Θ(k|E| log |V|) time, supporting Θ(log k) queries where k counts the distinct paths that are shortest over nontrivial intervals.