# lecture 13 - Math 482(Lecture 13 The shortest path...

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Math 482 (Lecture 13): The shortest path algorithm This lecture discusses the shortest path algorithm and its formulation as an LP. (This covers Section 3.4 of the textbook.) Wikipedia entry on the shortest path LP. (I found this clearer than the textbook.) The basic problem: You want to travel from source position s to termination position t. There are a bunch of different roads you can take. You want to take a path that has the least cost (e.g., cost might mean distance, or it might mean tolls.) Seattle to Kettle River range. Solutions to this problem used in: e.g., Google maps , Car GPS . Mathematical formulation: A weighted directed graph is a graph with * node set V * edge set E where each edge (also called arc ) e=(i,j) is directed i->j * each arc is assigned a weight c e Note: if you want a "two way street" between nodes i and j, you can have arcs i->j and j- >i. A path from s to t is a sequence of arcs s=i 0 ->i 1 ->i 2 ->. ..->i k-1 ->t=i k Shortest path problem (again): Find the path from s to t such that c (i0 -> i1) + c (i1 -> i1) +...+c (ik-1 -> ik) is minimized. In class exercise (the LP formulation):

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lecture 13 - Math 482(Lecture 13 The shortest path...

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