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Lecture15

# Lecture15 - Algorithms in Systems Engineering IE170 Lecture...

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Algorithms in Systems Engineering IE170 Lecture 15 Dr. Ted Ralphs

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IE170 Lecture 15 1 References for Today’s Lecture Required reading CLRS Chapter 22 References R. Sedgewick, Algorithms in C++ (Third Edition), 1998.
IE170 Lecture 15 2 Searching a Graph In the last lecture, we introduced a method of searching a graph using a technique called depth-first search (DFS). Graph search is a generalization of this method that is used to study the structure of a graph. We have already used graph search on several occasions. In the next few lectures, we will consider several methods of searching a graph. Each method will reveal something different about the structure of the graph. Many, many algorithms are based on this general framework. Finding a (shortest) path between two vertices in a graph . Determining whether a graph has a cycle . Determining a minimal set of edges that connect all the vertices . Determining whether there is a single edge/vertex whose removal disconnects the graph .

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IE170 Lecture 15 3 General Graph Search Graph search consists of systematically processing the vertices of a graph to discover some property of the graph. To search a single component: Choose a start vertex and add it to the list of unprocessed vertices. Repeat until no vertices remain on the list. * Choose a vertex v from the list of unprocessed vertices .
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