  A solution of the $k$ shortest paths problem may output paths that are
identical up to a single edge. On the other hand, a solution of the $k$
independent shortest paths problem consists of paths that share neither an edge
nor an intermediate node. We investigate the case in which the number of edges
that are not shared among any two paths in the output $k$-set is a parameter.
We study two main directions: exploring \emph{near-shortest} paths and
exploring \emph{exactly shortest paths}. We assume that the weighted graph
$G=(V,E,w)$ has no parallel edges and that the edge lengths (weights) are
positive. Our results are also generalized to the cases of $k$ shortest paths
where there are several weights per edge, and the results should take into
account the multi-criteria prioritized weight.
