Two-phase Algorithms for the Parametric Shortest Path Problem

Abstract. A 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 edgeweighted 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 preprocessing phase whose input is a parametric weighted graph, and whose output is a data structure, the advice, that is later used by the instantiation phase, where a specific value for the variable is given. The instantiation phase outputs the solution to the (standard) weighted graph problem that arises from the instantiation. The goal is to have the running time of the instantiation phase supersede the running time of any algorithm that solves the weighted graph problem from scratch, by taking advantage of the advice. In this paper we construct several parametric algorithms for the short...

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Sourav Chakraborty, Eldar Fischer, Oded Lachish, Raphael Yuster
• Keywords: Instantiation Phase, Parametric Weighted Graph, STACS 2010, Theoretical Computer Science, Weighted Graph