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Unformatted text preview: 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 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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This note was uploaded on 08/06/2008 for the course IE 170 taught by Professor Ralphs during the Spring '07 term at Lehigh University .
- Spring '07
- Systems Engineering