A comprehensive survey on the quickest path problem

Abstract

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

Algorithms for the quickest path problem and the reliable quickest path problem

“…On the other hand, there are algorithms which compute the first K shortest paths according to lead time for certain subnetworks of G. Then, they are sorted in accordance with the transmission time and the K best ones are selected. This is the general idea underlying the algorithm by Chen (1994) and the variant proposed by Pascoal et al (2006). These algorithms avoid having to compute quickest paths and so can directly use the routines developed to enumerate the first K shortest paths (Lawler 1976;Yen 1971), but at the price of usually computing more paths and managing more complex storing and ranking.…”

“…In order to design the algorithms to solve the RQPP, we have selected the algorithms by Rosen et al (1991) and by Pascoal et al (2006). We have implemented them using the ideas of Lawler's algorithm (1976) to compute the first K shortest paths.…”

“…As a result, the RQPP can be solved by using the algorithms by Rosen et al (1991) and by Pascoal et al (2006) with the modified partitioning rule described above in order to find the first quickest path verifying the constraint on reliability. We denote these algorithms by RQPPA 2 and RQPPA 3 , respectively.…”

The energy-constrained quickest path problem

“…The problem of computing the quickest path whose reliability is not lower than a given threshold has been analyzed in [2]. Pascoal et al [14] provide a survey on the subject.…”

Computational experiments with a lazy version of a K quickest simple path ranking algorithm

“…The procedures to solve this problem are either inspired by quickest path algorithms (Chen 1994), or adaptations of ranking shortest simple path algorithms (Pascoal et al 2005;Rosen et al 1991). The two types of methods cannot be compared, but recently a lazy version of Chen's algorithm comparable with both has been suggested (Pascoal et al 2006) (or Pascoal et al 2004 in an earlier version). The purpose of this work is to evaluate the performance of the variant of Chen's algorithm and to compare it with the existent methods.…”