Abstract
A weighted edge-coloured 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 edge-coloured graph. Additionally, a bound is presented on the expected number of minimal paths in weighted edge–bicoloured graphs. These bounds indicate that despite weighted edge-coloured graphs are theoretically intractable, amenability to computation is typically found in practice.
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This research was partly supported by Católica del Maule University Through the Project MECESUP–UCM0205.
This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.
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Ensor, A., Lillo, F. On the Tractability of Shortest Path Problems in Weighted Edge-Coloured Graphs. J Syst Sci Complex 31, 527–538 (2018). https://doi.org/10.1007/s11424-017-6138-0
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DOI: https://doi.org/10.1007/s11424-017-6138-0