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.
Keywords Bicriteria problem . Minsum-maxmin . Quickest path . Paths rankingThe quickest path problem is a particular case of optimal path problems, whose objective function evaluates the time taken to transmit a given amount of data through each path. This function depends on two parameters, an additive function that represents the path delay, and a bottleneck function that represents the path capacity or bandwidth. Thus, the resolution of