### Two-phase Algorithms for the Parametric Shortest Path Problem

Sourav Chakraborty, Eldar Fischer, Oded Lachish & Raphael Yuster
A {\em parametric weighted graph} is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edge-weighted graph. Parametric weighted graph problems are generalizations of weighted graph problems, and arise in various natural scenarios. Parametric weighted graph algorithms consist of two phases. A {\em preprocessing phase} whose input is a parametric weighted graph, and whose output is a data structure,...
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