Counting the number of minimal paths in weighted coloured-edge graphs
| aut.researcher | Ensor, Andrew | |
| dc.contributor.author | Ensor, A | |
| dc.contributor.author | Lillo, F | |
| dc.date.accessioned | 2011-12-13T10:50:21Z | |
| dc.date.available | 2011-12-13T10:50:21Z | |
| dc.date.copyright | 2011 | |
| dc.date.issued | 2011 | |
| dc.description.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. | |
| dc.identifier.citation | arXiv:1112.3066 [math.CO] | |
| dc.identifier.issn | 0166-218X (print) | |
| dc.identifier.uri | https://hdl.handle.net/10292/3083 | |
| dc.publisher | arXiv, Cornell University | |
| dc.relation.uri | http://arxiv.org/abs/1112.3066 | |
| dc.rights | NOTICE: this is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in (see Citation). The original publication is available at (see Publisher's Version) | |
| dc.rights.accessrights | OpenAccess | |
| dc.subject | Graph theory | |
| dc.subject | Minimal paths | |
| dc.subject | Multimodal network | |
| dc.subject | Transportation modes | |
| dc.subject | Weighted coloured-edge graph | |
| dc.title | Counting the number of minimal paths in weighted coloured-edge graphs | |
| dc.type | Journal Article | |
| pubs.organisational-data | /AUT | |
| pubs.organisational-data | /AUT/Design & Creative Technologies | |
| pubs.organisational-data | /AUT/Design & Creative Technologies/School of Computing & Mathematical Science | |
| pubs.organisational-data | /AUT/PBRF Researchers | |
| pubs.organisational-data | /AUT/PBRF Researchers/Design & Creative Technologies PBRF Researchers | |
| pubs.organisational-data | /AUT/PBRF Researchers/Design & Creative Technologies PBRF Researchers/DCT C & M Mathematical Science |