Effectively Counting s-t Simple Paths in Directed Graphs

TL;DR

This paper introduces a pruning technique to efficiently count s-t simple paths in directed graphs, significantly reducing search space and enhancing existing algorithms' performance through empirical validation.

Contribution

It presents a novel pruning method that improves s-t simple path counting efficiency and can be integrated with existing algorithms as a fast preprocessing step.

Findings

High empirical efficiency demonstrated on multiple networks

Effective reduction of search space in path counting

Compatible with existing algorithms for improved performance

Abstract

An important tool in analyzing complex social and information networks is s-t simple path counting, which is known to be #P-complete. In this paper, we study efficient s-t simple path counting in directed graphs. For a given pair of vertices s and t in a directed graph, first we propose a pruning technique that can efficiently and considerably reduce the search space. Then, we discuss how this technique can be adjusted with exact and approximate algorithms, to improve their efficiency. In the end, by performing extensive experiments over several networks from different domains, we show high empirical efficiency of our proposed technique. Our algorithm is not a competitor of existing methods, rather, it is a friend that can be used as a fast pre-processing step, before applying any existing algorithm.