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arXiv · 1112.3066

Counting the Number of Minimal Paths in Weighted Coloured-Edge Graphs

Andrew Ensor·Felipe Lillo
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Abstract

A weighted coloured-edge graph is a graph for which each edge is assigned both a positive weight and a discrete colour, and can be used to model transportation and computer networks in which there are multiple transportation modes. In such a graph paths are compared by their total weight in each colour, resulting in a Pareto set of minimal paths from one vertex to another. This paper will give a tight upper bound on the cardinality of a minimal set of paths for any weighted coloured-edge graph. Additionally, a bound is presented on the expected number of minimal paths in weighted bicoloured-edge graphs.

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BibTeXRIS

Andrew Ensor, Felipe Lillo. 2011-12-13. Counting the Number of Minimal Paths in Weighted Coloured-Edge Graphs. https://arxiv.org/abs/1112.3066

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