Implementations and empirical comparison of K shortest loopless path algorithms

The first work on the network optimisation problem of rankingK shortest paths, K ∈ IN, appeared in 1959, more or less simultaneously with the first papers on the shortest path problem. Since then the particular problem (when K = 1) has merited much more attention than its generalisation. Nevertheless, several titles are included on the very complete bibliography about theK shortest paths problem, online at http://www.ics.uci.edu/∼eppstein/bibs/kpath.bib, many of them concerning problems related with the K shortest paths problem and real word applications. With the development of computers and data structures there has been an increasing interest from the researchers on this problem, as larger problems resulting from real world applications, demanding more space of memory as well as quick responses, can now be solved. In this paper we focus on the K shortest loopless paths problem, the variant where paths are not allowed to have repeated nodes. We survey algorithms for this problem, introduce a new method to solve it, and compare empirically their implementations.