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

TL;DR

This paper presents an efficient implementation of Fishburn's algorithm for solving difference constraint systems with variables restricted to a finite set, achieving a runtime of O(n+km).

Contribution

The authors provide a practical implementation of Fishburn's algorithm with optimized runtime complexity for finite set variable constraints.

Findings

Implementation runs in O(n+km) time.

Efficient solution for systems with finite set variables.

Improved practical performance of difference constraint solving.

Abstract

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.