# A Parallel Genetic Algorithm for Book Embedding

## Faculty Sponsor

Paul DePalma and Shannon Overbay, Gonzaga University

## Research Project Abstract

Assuming a circular ordering of a graph's vertices, a book embedding is defined as an assignment of colors to the graph's edges, such that no same-colored edges intersect. The minimum number of colors required to produce a valid book embedding is the graph's book thickness. Computing the book thickness of an arbitrary graph is generally intractable by brute force means, so we use genetic algorithms to find approximate solutions. A genetic algorithm (GA) walks through the search space with a population of candidate solutions, in a manner loosely inspired by biological evolution.

We present a simple GA (written in C++) for approximating the optimum book thickness of a graph with fixed vertex ordering. We also give our preliminary results with a massively parallel GA on the CUDA architecture, which is approximately 3x faster than the single-threaded GA.

## Session Number

SS1B

## Location

Robinson 310

## Abstract Number

SS1B-e

A Parallel Genetic Algorithm for Book Embedding

Robinson 310

Assuming a circular ordering of a graph's vertices, a book embedding is defined as an assignment of colors to the graph's edges, such that no same-colored edges intersect. The minimum number of colors required to produce a valid book embedding is the graph's book thickness. Computing the book thickness of an arbitrary graph is generally intractable by brute force means, so we use genetic algorithms to find approximate solutions. A genetic algorithm (GA) walks through the search space with a population of candidate solutions, in a manner loosely inspired by biological evolution.

We present a simple GA (written in C++) for approximating the optimum book thickness of a graph with fixed vertex ordering. We also give our preliminary results with a massively parallel GA on the CUDA architecture, which is approximately 3x faster than the single-threaded GA.