Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles

TL;DR

This paper explores the benefits and complexities of allowing large-angle crossings in graph drawings with vertices at specified positions, focusing on different drawing styles and bend constraints.

Contribution

It analyzes the impact of large-angle crossings on computational complexity, curve complexity, and generality in point-set embeddings with various bend restrictions.

Findings

Allowing large-angle crossings can reduce complexity in certain graph drawings.

Different bend constraints affect the feasibility of large-angle crossing drawings.

Results vary across drawing styles with one, two, or three bends per edge.

Abstract

Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. In this paper, we consider problems in the intersection of these two areas. Given the point-set-embedding scenario, we are interested in how much we gain in terms of computational complexity, curve complexity, and generality if we allow large-angle crossings as compared to the planar case. We investigate two drawing styles where only bends or both bends and edges must be drawn on an underlying grid. We present various results for drawings with one, two, and three bends per edge.