Finding the k shortest simple paths: A new algorithm and its implementation

  • Authors:

  • John Hershberger;Matthew Maxel;Subhash Suri

  • Affiliations:

  • Mentor Graphics Corporation, Wilsonville, OR;University of California at Santa Barbara, Santa Barbara, CA;University of California at Santa Barbara, Santa Barbara, CA

  • Venue:
  • ACM Transactions on Algorithms (TALG)
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

We describe a new algorithm to enumerate the k shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on a replacement paths algorithm proposed by Hershberger and Suri [2001], and can yield a factor Θ(n) improvement for this problem. But there is a caveat: The fast replacement paths subroutine is known to fail for some directed graphs. However, the failure is easily detected, and so our k shortest paths algorithm optimistically uses the fast subroutine, then switches to a slower but correct algorithm if a failure is detected. Thus, the algorithm achieves its Θ(n) speed advantage only when the optimism is justified. Our empirical results show that the replacement paths failure is a rare phenomenon, and the new algorithm outperforms the current best algorithms; the improvement can be substantial in large graphs. For instance, on GIS map data with about 5,000 nodes and 12,000 edges, our algorithm is 4--8 times faster. In synthetic graphs modeling wireless ad hoc networks, our algorithm is about 20 times faster.