Presented by: Zuzana Kubinova

1. Graph Theory Application - Not
Only for Engineering Problems
Zuzana Kubínová, HTS, 11-9-2012

2. HONEYWELL - CONFIDENTIAL
About The Speaker
•Master's degree in Mathematical Engineering
obtained at Brno University of Technology
•Spent six months studying abroad in 2008 - in
UK Nottingham Trent University
•Diploma thesis Analysis of Data Flow in the
Fly-by-Wire System written for Honeywell
•Systems Engineer for Honeywell Technical
Solutions (HTS CZ) in Brno, Czech Republic
since May 2009

3. HONEYWELL - CONFIDENTIAL
Why Is This Relevant To Me?
• Finishing school is never the end of learning.
• Every company needs innovation. Not only
innovation of products but also innovation of
processes. Be the one with out of the box ideas
and bring your company growth. Become a
competitive advantage for your company!
• Graphs describe relations. In many parts of your
life and work there are relations, therefore there is
a good chance to use graphs and graph
algorithms.
• There are ways to bake a cake and there are
ways to analyze and make decisions. Let's
explore!

4. HONEYWELL - CONFIDENTIAL
Introduction
• The Graph Theory started in a paper published in
1736 by the Swiss mathematician Leonhard Euler
• Problem known as Seven bridges of Koningsberg 1
1
Picture from www.uh.edu

5. HONEYWELL - CONFIDENTIAL
Introduction
•Graphs versus Charts
• Charts
• Graphs from a mathematical point of view
• G=(N,E,ε), where N is a set of nodes, E is a set of edges
and
ε:E N x N is a mapping
• In accordance with characteristics of ε we can model
several types of graphs - e.g. simple graph, multigraph or
directed graph

6. HONEYWELL - CONFIDENTIAL
Basic Types Of Graphs
• Simple
graph
• Multigraph • Directed graph
(digraph)

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Graph – Graphical And Non-Graphical
Representation
• Graphical representation 1
• Non-Graphical representation
• it is what makes the Graph Theory so powerful
• allows handle large data effectively
• Edge list, Adjacency list, Adjacency matrix
1
Both graphs from www.graphviz.org

8. HONEYWELL - CONFIDENTIAL
A House By One Line
• Do you know how to draw a house by one line?
• Do you know if it is possible at all?

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A House By One Line
• How about these?
• Euler path – it exists if and only if each node has even
number of edges or there are exactly two nodes with
odd number of edges.

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Back To Seven Bridges Of Koningsberg
• So, is it possible to cross all the bridges only once and
get back home?
• How would you modify it?

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Students And Graph Coloring
• Problem:
Arrange the students’ sitting in a classroom such that
they can’t copy from each other during a test.

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Students And Graph Coloring
• Graph Coloring
• Any two adjacent nodes are assigned a different
color.
• If you use k colors, we call the graph k-colorable.
• Goal is to minimize k – use as little colors as
possible.

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Students And Graph Coloring
Graph Coloring

14. 4 HONEYWELL - CONFIDENTIAL
Path Search Algorithms
• Used for variety of tasks – e.g. shortest path search, search for
existing path, search in timetables, find steps to solve the Rubik’s
Cube…

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Path Search Algorithms
… and their use in Honeywell Aero Flight Control division

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Path Search Algorithm
System is really complicated …
• Using search path
algorithms saves lots of
time, money and sanity of
engineers 

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Summary
• The Graph Theory is a fascinating branch of
mathematics suitable for many engineering
applications.
• Mr Euler's story shows that even amusing little
brainteasers can give rise to a new and very useful
theory.
• Appropriate use of graph algorithms can be very
benefiting.

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Q & A

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Thank you for your attention.