The problem of listing the K shortest simple (loopless) st-paths in a
graph has been studied since the early 1960s. For a non-negatively weighted
graph with n vertices and m edges, the most efficient solution is an
O(K(mn+n2logn)) algorithm for directed graphs by Yen and Lawler
[Management Science, 1971 and 1972], and an O(K(m+nlogn)) algorithm for
the undirected version by Katoh et al. [Networks, 1982], both using O(Kn+m)
space. In this work, we consider a different parameterization for this problem:
instead of bounding the number of st-paths output, we bound their length. For
the bounded length parameterization, we propose new non-trivial algorithms
matching the time complexity of the classic algorithms but using only O(m+n)
space. Moreover, we provide a unified framework such that the solutions to both
parameterizations -- the classic K-shortest and the new length-bounded paths
-- can be seen as two different traversals of a same tree, a Dijkstra-like and
a DFS-like traversal, respectively.Comment: 12 pages, accepted to IWOCA 201