Counting the number of minimal paths in weighted coloured-edge graphs
Ensor, A; Lillo, F
Permanent link
http://hdl.handle.net/10292/3083Metadata
Show full metadataAbstract
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.