Simultaneous Embeddings with Few Bends and Crossings

Simultaneous Embeddings with Few Bends and Crossings

A simultaneous embedding with fixed edges (SEFE) of two planar graphs R and B is a pair of plane drawings of R and B that coincide when restricted to the common vertices and edges of R and B. We show that whenever R and B admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve with few bends and every pair of edges has few crossings. Specifically: (1) if R and B are trees ...

Simultaneous Drawing of Planar Graphs with Right-Angle Crossings and Few Bends

Given two planar graphs that are defined on the same set of vertices, a RAC simultaneous drawing is a drawing of the two graphs where each graph is drawn planar, no two edges overlap, and edges of one graph can cross edges of the other graph only at right angles. In the geometric version of the problem, vertices are drawn as points and edges as straight-line segments. It is known, however, that...

Simultaneous Embedding of Planar Graphs with Few Bends

We consider several variations of the simultaneous embedding problem for planar graphs. We begin with a simple proof that not all pairs of planar graphs have simultaneous geometric embedding. However, using bends, pairs of planar graphs can be simultaneously embedded on the O(n) × O(n) grid, with at most three bends per edge, where n is the number of vertices. The O(n) time algorithm guarantees...

Drawing Simultaneously Embedded Graphs with Few Bends

Computing Storyline Visualizations with Few Block Crossings

Storyline visualizations show the structure of a story, by depicting the interactions of the characters over time. Each character is represented by an x-monotone curve from left to right, and a meeting is represented by having the curves of the participating characters run close together for some time. There have been various approaches to drawing storyline visualizations in an automated way. I...