A nonenumerative algorithm to find the k longest (shortest) paths in a DAG
Data Structures and Algorithms
2013-01-03 v1
Abstract
In this paper, we present a novel and efficient algorithm to find the k longest (shortest) paths between sources and sinks in a directed acyclic graph (DAG). The algorithm does not enumerate paths therefore it is especially useful for very large k values. It is based on the Valued-Sum-of-Product (VSOP) tool, which is an extension of Zero-suppressed Binary Decision Diagrams (ZBDDs). We assessed the performance of this algorithm with a DAG model of a path-intensive combinational circuit, viz. c6288, that has \sim10^{20} paths. We found that it took about 64 minutes to compute all paths in this DAG along with their lengths.
Cite
@article{arxiv.1301.0181,
title = {A nonenumerative algorithm to find the k longest (shortest) paths in a DAG},
author = {Fatih Kocan},
journal= {arXiv preprint arXiv:1301.0181},
year = {2013}
}