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MIT OpenCourseWare http://ocw.mit.edu 6.006 Introduction to Algorithms Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Lecture 12 Searching I: Graph Search & Representations 6.006 Spring 2008 Lecture 12: Searching I: Graph Search and Representations Lecture Overview: Search 1 of 3 Graph Search Applications Graph Representations Introduction to breadth-first and depth-first search Readings CLRS 22.1-22.3, B.4 Graph Search Explore a graph e.g., find a path from start vertices to a desired vertex Recall : graph G = ( V, E ) V = set of vertices (arbitrary labels) E = set of edges i.e. vertex pairs ( v, w ) ordered pair = directed edge of graph unordered pair = undirected a b c d a b c UNDIRECTED DIRECTED e.g. V = {a,b,c,d} E = {{a,b},{a,c}, {b,c},{b,d}, {c,d}} V = {a,b,c} E = {(a,c),(b,c), (c,b),(b,a)} Figure 1: Example to illustrate graph terminology 1
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Lecture 12 Searching I: Graph Search & Representations 6.006 Spring 2008 Applications: There are many. web crawling ( How Google finds pages ) social networking ( Facebook friend finder ) computer networks ( Routing in the Internet ) shortest paths [next unit] solving puzzles and games checking mathematical conjectures Pocket Cube:
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