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The color-constrained and interchange-constrained shortest path problems

Nassim Dehouche (nassim.deh***at***mahidol.ac.th)

Abstract: We study two variants of the shortest path problem. Given an integer k, the k-color-constrained and the k-interchange-constrained shortest path problems, respectively seek a shortest path that uses no more than k colors and one that makes no more than k − 1 alternations of colors. We show that the former problem is NP-hard, when the latter is tractable. The study of these problems is motivated by some limitations in the use of diameter-based metrics as quality indicators for transit networks. We notably show that indicators such as the diameter or directness of a transit network fail to adequately account for travel convenience in measuring the connectedness of a network and propose a new network indicator, based on solving the k-interchange-constrained shortest path problem, that aims at alleviating these limitations.

Keywords: Graph Theory, Shortest Path Problem, Transit Networks

Category 1: Applications -- OR and Management Sciences (Transportation )

Category 2: Combinatorial Optimization (Graphs and Matroids )

Category 3: Network Optimization

Citation: Technical Report, Mahidol University International College, Health Administration Research Cluster, Technical Report Number 1

Download: [PDF]

Entry Submitted: 03/02/2018
Entry Accepted: 03/03/2018
Entry Last Modified: 04/26/2018

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