Planar L-Drawings of Directed Graphs

TL;DR

This paper investigates planar L-drawings of directed graphs, establishing necessary conditions, proving NP-completeness of their existence test, and providing linear-time algorithms for upward-planar cases based on specific st-orderings.

Contribution

It introduces necessary conditions for planar L-drawings, proves the NP-completeness of their existence testing, and offers efficient algorithms for upward-planar L-drawings based on st-orderings.

Findings

Testing for planar L-drawings is NP-complete.

Directed st-graphs with upward-planar L-drawings have specific st-orderings.

Linear-time algorithms compute or determine the absence of such orderings.

Abstract

We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. Motivated by this result, we focus on upward-planar L-drawings. We show that directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering. We give a linear-time algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.