An experimental study on approximating kshortest simple paths

We have conducted an extensive experimental study on approximation algorithms for computing k shortest simple paths in weighted directed graphs. Very recently, Bernstein [2010] presented an algorithm that computes a 1 + ε approximated k shortest simple path in O(ε^-1k(m + nlog n)log² n) time. We have implemented Bernstein's algorithm and tested it on synthetic inputs and real-world graphs (road maps). Our results reveal that Bernstein's algorithm has a practical value in many scenarios. Moreover, it produces in most of the cases exact paths rather than approximated. We also present a new variant for Bernstein's algorithm. We prove that our new variant has the same upper bounds for the running time and approximation as Bernstein's original algorithm. We have implemented and tested this variant as well. Our testing shows that this variant, which is based on a simple theoretical observation, is better than Bernstein's algorithm in practice.