The application domains like network connection routing, highway and power line engineering, robot motion planning and other optimization problems require the computation of shortest path. Computations of K-shortest paths provide more (K-1) numbers of backup shortest paths for consideration, which enable the applicability of additional constraints on the particular domains. For instance, a biologist can determine the best of an alignment from the available instances of biological sequence alignments generated from more than one shortest paths computation. The purpose of this paper is to provide a comprehensive review of existing algorithms available for K-shortest paths computation. It will be useful for researcher to implement the effective K-shortest paths computation based on their matching computational requirements over the domain of their interest.

In this note we are concerned with the ranking of shortest loopless paths problem. It is shown that in general this problem does not satisfy the optimality principle and as a consequence only methods based on the computation of a super set of the set of the K shortest loopless paths are valid. It is shown how this methods for the unconstrained problem can be adapted for determining the K shortest loopless paths.