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Lecture13 - Algorithms in Systems Engineering IE170 Lecture...

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Algorithms in Systems Engineering IE170 Lecture 13 Dr. Ted Ralphs
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IE170 Lecture 13 1 References for Today’s Lecture Required reading CLRS Chapter 21 and 22 References R. Sedgewick, Algorithms in C++ (Third Edition), 1998.
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IE170 Lecture 13 2 Connectivity Relations So far, we have only considered sets of items that are related to each other through some kind of ordering (if at all). In other words, two items x and y are only related by their relative positions in the ordered list. We will now generalize this idea by considering additional connectivity relationships between items. To do so, we will specify that there is a direct link between certain pairs of items. This will allow us to ask questions such as
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IE170 Lecture 13 3 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. There are several variations on this theme. The connections in the graph may or may not have an orientation or a direction . We may not allow more than one connection between a pair of items. We may 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.
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IE170 Lecture 13 4 Applications of Graphs
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IE170 Lecture 13 5 Graph Terminology and Notation In an undirected graph, the “items” are usually called vertices (sometimes
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