# Basser Seminar Series

# Area Proportional and Minimum Area Venn/Euler diagrams

**Frank Ruskey**

University of Victoria, Canada

Friday 1 February 2008, 2-3pm ****Note different day and time**

School of IT Building, Lecture Theatre, Room 123, Level 1

## Abstract

A "Venn diagram" is a collection of n simple closed curves with the property that each of the 2^n possible intersections of the interiors and exteriors of the curves is non-empty and topologically connected.

In an "Euler diagram" some of the intersections can be empty. After a brief introduction to some of the fundamental properties of Euler/Venn diagrams, this talk will focus on two general problems:

(A) drawing Euler diagrams in such a way that each intersection has a specified area relative to the others, and

(B) drawing Venn diagrams rectilinearly so that they have minimum area.

The diagrams from (A) are called "area proportional Venn diagrams". This problem has many applications and our results/software have been used by researchers in marketing, genomics, and medical statistics. Problem (B) has no application currently, but has beautiful results of intrinsic scientific interest.

Both areas have tantalizing open problems.

This is joint research with my students Stirling Chow and Bette Bultena.

## Speaker's biography

Frank Ruskey is a Professor of Computer Science at the University of Victoria, Canada.

His research interests and accomplishments are mainly in combinatorial algorithms and combinatorial mathematics, particularly Gray codes and Venn/Euler diagrams.

He is proud of the fact that his Steve Nash and Don Knuth numbers are both one.