SIAM Journal on Computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Vickrey Prices and Shortest Paths: What is an Edge Worth?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Finding the k shortest simple paths: A new algorithm and its implementation
ACM Transactions on Algorithms (TALG)
Oracles for Distances Avoiding a Failed Node or Link
SIAM Journal on Computing
Improved algorithms for the k simple shortest paths and the replacement paths problems
Information Processing Letters
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the $k$ Shortest Simple Paths Problem in Weighted Directed Graphs
SIAM Journal on Computing
Subcubic Equivalences between Path, Matrix and Triangle Problems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We have conducted an extensive experimental study on approximation algorithms for computing k shortest simple paths in weighted directed graphs. Very recently, Bernstein [2] presented an algorithm that computes a 1 + ε approximated k shortest simple paths in O(ε-1k(m + n log 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 show that this variant, which is based on a simple theoretical observation, is better than Bernstein's algorithm in practice.