Complexity of solving a system of difference constraints with variables restricted to a finite set

Fishburn developed an algorithm to solve a system of $m$ difference constraints whose $n$ unknowns must take values from a set with $k$ real numbers [Solving a system of difference constraints with variables restricted to a finite set, Inform Process Lett 82 (3) (2002) 143–144]. We provide an implementation of Fishburn’s algorithm that runs in $O(n+km)$ time.