Bounds on the Size of Sound Monotone Switching Networks Accepting Permutation Sets of Directed Trees

TL;DR

This paper establishes nearly optimal bounds on the size of sound monotone switching networks for permutation sets of directed trees, advancing understanding of monotone memory efficiency in specific directed graph problems.

Contribution

It provides almost tight bounds on the size of such networks, a novel result for the monotone complexity of directed ST-connectivity with restricted input graphs.

Findings

Bounds are nearly tight for the size of switching networks

Results apply to permutation sets of directed trees

Advances understanding of monotone memory efficiency

Abstract

In this paper, we prove almost tight bounds on the size of sound monotone switching networks accepting permutations sets of directed trees. This roughly corresponds to proving almost tight bounds bounds on the monotone memory efficiency of the directed ST-connectivity problem for the special case in which the input graph is guaranteed to have no path from s to t or be isomorphic to a specific directed tree.