Efficiently listing bounded length st-paths
Abstract
The problem of listing the $K$ shortest simple (loopless) $st$-paths in a graph has been studied since the early 1960s. For a non-negatively weighted graph with $n$ vertices and $m$ edges, the most efficient solution is an $O(K(mn + n^2 \log n))$ algorithm for directed graphs by Yen and Lawler [Management Science, 1971 and 1972], and an $O(K(m+n \log n))$ algorithm for the undirected version by Katoh et al. [Networks, 1982], both using $O(Kn + m)$ space. In this work, we consider a different parameterization for this problem: instead of bounding the number of $st$-paths output, we bound their length. For the bounded length parameterization, we propose new non-trivial algorithms matching the time complexity of the classic algorithms but using only $O(m+n)$ space. Moreover, we provide a unified framework such that the solutions to both parameterizations -- the classic $K$-shortest and the new length-bounded paths -- can be seen as two different traversals of a same tree, a Dijkstra-like and a DFS-like traversal, respectively.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2014
- DOI:
- 10.48550/arXiv.1411.6852
- arXiv:
- arXiv:1411.6852
- Bibcode:
- 2014arXiv1411.6852R
- Keywords:
-
- Computer Science - Data Structures and Algorithms
- E-Print:
- 12 pages, accepted to IWOCA 2014