A comprehensive survey on the quickest path problem

This work is a survey on a special minsum-maxmin bicriteria problem, known as the quickest path problem, that can model the transmission of data between two nodes of a network. Moreover, the authors review the problems of ranking the K quickest paths, and the K quickest loopless paths, and compare them in terms of the worst-case complexity order. The classification presented led to the proposal of a new variant of a known K quickest loopless paths algorithm. Finally, applications of quickest path algorithms are mentioned, as well as some comparative empirical results. This work was partially supported by FEDER and OE, under the projects POCTI/MAT/139/2001, POCTI/ISFL-1/152, POSI/SRI/37346/2001, and POCTI/MAT/37707/2001.