  This article generalizes the Near Shortest Paths Problem introduced by Byers
and Waterman in 1984 using concepts of the Universal Shortest Path Problem
established by Turner and Hamacher in 2011. The generalization covers a variety
of shortest path problems by introducing a universal weight vector. We apply
this concept to the Near Shortest Paths Problem in a way that we are able to
enumerate all universal near shortest simple paths. We present two recursive
algorithms to compute the set of universal near shortest simple paths between
two prespecified vertices and evaluate the running time complexity per path
enumerated with respect to different values of the universal weight vector.
Further, we study the cardinality of a minimal complete set with respect to
different values of the universal weight vector.
