Graph Theory
Breadth First Search
IE170: Algorithms in Systems Engineering:
Lecture 15
Jeff Linderoth
Department of Industrial and Systems Engineering
Lehigh University
February 26, 2007
Jeff Linderoth
IE170:Lecture 15
Graph Theory
Breadth First Search
Taking Stock
Last Time
DP for Lot Sizing
Greedy Algorithm for activity scheduling
This Time
The Wonderful World of Graph Theory
You should read Chap 22
Jeff Linderoth
IE170:Lecture 15
Graph Theory
Breadth First Search
Graphs
A
graph
is an abstract object used to model such connectivity
relations.
A
graph
consists of a list of items, along with a set of
connections between the items.
The study of such graphs and their properties, called
graph
theory
, is hundreds of years old.
Graphs can be visualized easily by creating a physical
manifestation showing the connection relationships
Jeff Linderoth
IE170:Lecture 15
Graph Theory
Breadth First Search
Graph Types
The connections in the graph may or may not have an
orientation
or a
direction
.
We may (or may not) allow more than one connection
between a pair of items
We may (or may not) not allow an item to be connected to
itself.
For now, we consider graphs that are
undirected
, i.e., the connections do not have an orientation,
and
simple
, i.e., we allow only one connection between each pair of
items and no connections from an item to itself.
Jeff Linderoth
IE170:Lecture 15
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Graph Theory
Breadth First Search
(A few) Applications of Graphs
Maps
Internet/World Wide Web
Social Networks
Circuits
Scheduling
Communication Networks
Matching and Assignment
Chemistry and Physics
Jeff Linderoth
IE170:Lecture 15
Graph Theory
Breadth First Search
Graph Terminology and Notation
In an undirected graph, the “items” are usually called
vertices
(sometimes also called
nodes
).
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 Spring '07
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 Graph Theory, Systems Engineering, Lehigh University, breadth first search, Jeff Linderoth

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