(Quasi-)linear time algorithm to compute LexDFS, LexUP and LexDown orderings

TL;DR

This paper presents efficient algorithms for computing LexDFS, LexUP, and LexDOWN graph orderings, achieving linear or near-linear time complexity, improving the efficiency of these graph search methods.

Contribution

It introduces a linear time algorithm for LexUP orderings and near-linear algorithms for LexDOWN and LexDFS orderings, enhancing computational efficiency.

Findings

LexUP orderings computed in linear time

LexDOWN and LexDFS orderings computed in $n + m \,\log m$ time

Algorithms improve efficiency of graph search orderings

Abstract

We consider the three graph search algorithm LexDFS, LexUP and LexDOWN. We show that LexUP orderings can be computed in linear time by an algorithm similar to the one which compute LexBFS. Furthermore, LexDOWN orderings and LexDFS orderings can be computed in time $\left(n+m\log m\right)$ where $n$ is the number of vertices and $m$ the number of edges.