  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
$O(K(mn + n^2 \log n))$ algorithm for directed graphs by Yen and Lawler
[Management Science, 1971 and 1972], and an $O(K(m+n \log n))$ 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.
