DeepAI
Log In Sign Up

Rectilinear Planarity of Partial 2-Trees

08/26/2022
by   Walter Didimo, et al.
0

A graph is rectilinear planar if it admits a planar orthogonal drawing without bends. While testing rectilinear planarity is NP-hard in general, it is a long-standing open problem to establish a tight upper bound on its complexity for partial 2-trees, i.e., graphs whose biconnected components are series-parallel. We describe a new O(n^2 log^2 n)-time algorithm to test rectilinear planarity of partial 2-trees, which improves over the current best bound of O(n^3 log n). Moreover, for series-parallel graphs where no two parallel-components share a pole, we are able to achieve optimal O(n)-time complexity. Our algorithms are based on an extensive study and a deeper understanding of the notion of orthogonal spirality, introduced in 1998 to describe how much an orthogonal drawing of a subgraph is rolled-up in an orthogonal drawing of the graph.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/09/2020

Rectilinear Planarity Testing of Plane Series-Parallel Graphs in Linear Time

A plane graph is rectilinear planar if it admits an embedding-preserving...
07/31/2019

Level-Planar Drawings with Few Slopes

We introduce and study level-planar straight-line drawings with a fixed ...
10/01/2021

Spirality and Rectilinear Planarity Testing of Independent-Parallel SP-Graphs

We study the long-standing open problem of efficiently testing rectiline...
08/17/2015

Knuthian Drawings of Series-Parallel Flowcharts

Inspired by a classic paper by Knuth, we revisit the problem of drawing ...
06/05/2021

Upward planar drawings with two slopes

In an upward planar 2-slope drawing of a digraph, edges are drawn as str...
10/10/2022

Parameterized Approaches to Orthogonal Compaction

Orthogonal graph drawings are used in applications such as UML diagrams,...
01/22/2020

Drawing Prolog Search Trees: A Manual for Teachers and Students of Logic Programming

Programming in Prolog is hard for programmers that are used to procedura...