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Fast computation of Q‐value‐based dynamic programming on road networks

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TLDR
A Q‐value‐based dynamic programming using the division concept for solving both single and multiple shortest path problems on road networks, which can greatly save the computational time without any preprocessing on the road networks.
Abstract
One of the essential components of vehicle navigation systems is route planning. The single shortest path problem and multiple shortest path problem have been widely studied for route planning. This paper introduces a Q-value-based dynamic programming using the division concept for solving both single and multiple shortest path problems on road networks. The proposed algorithm divides the whole network into different divisions, and the updating of Q values in each division is one stage for searching the optimal routes on road networks. The proposed algorithm can greatly save the computational time without any preprocessing on the road networks. The proposed algorithm is also systematically studied in various sizes of road networks. The simulation results show the efficiency and effectiveness of the proposed algorithm on large-scale road networks. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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A note on two problems in connexion with graphs

TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Journal ArticleDOI

On the Theory of Dynamic Programming

TL;DR: This paper is the text of an invited address before the annual summer meeting of the American Mathematical Society at Laramie, Wyoming, September 2, 1954, of an expository nature on the theory of dynamic programming.
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Finding the k Shortest Paths

TL;DR: K shortest paths are given for finding the k shortest paths connecting a pair of vertices in a digraph, and applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery are described.
Journal ArticleDOI

The theory of dynamic programming

TL;DR: The text of an invited address before the annual summer meeting of the American Mathematical Society at Laramie, Wyoming, September 2, 1954 is given in this article, where the contents are chiefly of an expository nature on the theory of dynamic programming.