Counting the Number of Minimal Paths in Weighted Coloured-Edge Graphs
Combinatorics
2011-12-15 v1 Discrete Mathematics
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.
Cite
@article{arxiv.1112.3066,
title = {Counting the Number of Minimal Paths in Weighted Coloured-Edge Graphs},
author = {Andrew Ensor and Felipe Lillo},
journal= {arXiv preprint arXiv:1112.3066},
year = {2011}
}