The construction of all the projective spanning trees of a given digraph

TL;DR

This paper presents algorithms for constructing all projective rooted spanning trees of a digraph, with applications in analyzing syntactic subordination in linguistics.

Contribution

It introduces new algorithms that reduce the problem to maximal independent sets and grow spanning trees step-by-step, enhancing analysis of linguistic structures.

Findings

Algorithms successfully construct all projective spanning trees.

Applied to syntactic analysis of noun subordination.

Provides a systematic method for linguistic structure analysis.

Abstract

In the present paper we consider the problem of constructing all the projective rooted spanning trees of a given graph. We propose an algorithm based on reducing this problem to the problem of constructing all the maximal independent sets of a certain derived graph. We also offer an algorithm for step-by-step growing the spanning trees that sifts, at each step, any sub-trees non-extendable to projective spanning trees. The proposed algorithms were applied for analyzing the possible variants of the syntactic subordination of nouns through prepositions .