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

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.

preprint2011arXivOpen access
Andrew EnsorFelipe Lillo
math.CODiscrete Mathematics
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Andrew EnsorFelipe Lillo

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