Linear Time Split Decomposition Revisited

TL;DR

This paper revisits the problem of designing a simple linear time algorithm for undirected graph split decomposition, providing insights and potentially improved methods for this fundamental graph problem.

Contribution

The paper presents a new approach or revisits existing methods to achieve linear time complexity for split decomposition in undirected graphs.

Findings

Achieved or improved linear time algorithm for split decomposition

Enhanced understanding of orthogonal families in graph decompositions

Potential simplification of existing algorithms

Abstract

Given a family F of subsets of a ground set V, its orthogonal is defined to be the family of subsets that do not overlap any element of F. Using this tool we revisit the problem of designing a simple linear time algorithm for undirected graph split (also known as 1-join) decomposition.