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Policy Iteration Algorithm For Shortest Path Problems

By Jean Cochet-terrasson and Stéphane Gaubert


. The shortest paths tree problem consists in finding a spanning tree rooted at a given node, in a directed weighted graph, such that for each node i , the path of the tree which goes from i to the root has minimal weight. We propose an algorithm which is a deterministic version of Howard's policy iteration scheme. We show that policy iteration is faster than the Bellman (or value iteration) algorithm. In particular, the worst case execution time of policy iteration is O(nm), where n is the number of nodes, and m is the number of arcs. Policy iteration finds rapidly a circuit of negative weight when there is one. R esum e. Le probleme de l'arbre des plus courts chemins consiste a trouver un arbre couvrant de racine donnee dans un graphe oriente value, tel que pour tout sommet i , le chemin de l'arbre qui va de i a la racine a un poids minimum. Nous proposons un algorithme qui est une version deterministe de l'iteration sur les politiques d'Howard. Nous montrons que l'iteration sur les..

Topics: Minimal cost, shortest path, spanning tree, max-plus algebra, linear fixed point equations, deterministic optimal stopping, policy iteration, Howard algorithm
Year: 2007
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