Improved upper and lower bound techniques for monotone switching networks for directed connectivity

TL;DR

This paper advances the understanding of monotone switching networks for directed connectivity by establishing new upper and lower bounds, employing novel techniques to generalize previous results.

Contribution

It introduces new methods for analyzing the monotone space complexity of directed connectivity, significantly broadening the scope of prior bounds.

Findings

Established new upper bounds for monotone switching networks.

Derived lower bounds that improve on previous results.

Generalized bounds to a larger class of input graphs.

Abstract

In this paper, we analyze the monotone space of complexity of directed connectivity for a large class of input graphs $G$ using the switching network model. The upper and lower bounds we obtain are a significant generalization of previous results and the proofs involve several completely new techniques and ideas.