A nonenumerative algorithm to find the k longest (shortest) paths in a DAG

TL;DR

This paper introduces a novel nonenumerative algorithm leveraging VSOP and ZBDDs to efficiently find the k longest or shortest paths in large DAGs without path enumeration, demonstrated on a complex circuit model.

Contribution

The paper presents a new nonenumerative algorithm based on VSOP and ZBDDs for efficiently finding k longest or shortest paths in large DAGs, avoiding path enumeration.

Findings

Successfully computed all paths in a DAG with ~10^{20} paths in 64 minutes.

The algorithm is especially useful for large k values due to its nonenumerative nature.

Demonstrated effectiveness on a complex circuit model.

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.