Embedding graphs in non-Euclidean geometries

Summary

The mathematics of embeddings of graphs in non-Euclidean geometric spaces.

Supervisor(s)

Professor Peter Eades

Research Location

Information Technologies

Program Type

N/A

Synopsis

Most network visualization methods essentially embed graphs in either 2 or 3 dimensional Euclidean spaces (although hyperbolic spaces have been used in a minor way). The aim of the visualization mapping is to choose an embedding that optimizes one or more of a set of criteria, such as:a. Minimizing the number of edge crossingsb. Maximizing resolutionc. Maximizing symmetryThis project aims to make a mathematical study of embeddings of graphs in non-Euclidean spaces, using analogues of the usual visualization criteria for Euclidean embeddings. In particular, we will study embeddings in finite geometries.

Keywords

Discrete mathematics, geometry, graph, topology, algorithms

Opportunity ID

The opportunity ID for this research opportunity is: 399

Other opportunities with Professor Peter Eades

• Visual Analytics
• Geometric Algorithms
• Algorithmics for social networks
• Embeddings of graphs on arrangements of planes in three dimensions
• Drawing Algorithms for Almost Planar Graphs