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Unformatted text preview: Shortest Paths The Algorithms IE170: Algorithms in Systems Engineering: Lecture 21 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University March 21, 2007 Jeff Linderoth IE170:Lecture 21 Shortest Paths The Algorithms Taking Stock Last Time Shortest Paths TSP in Lab This Time Shortest Paths Jeff Linderoth IE170:Lecture 21 Shortest Paths The Algorithms Shortest Path Properties Shortest PathsDefinitions For the next few lectures, we will have a directed graph G = ( V,E ) , and a weight function w : E R | E | . We are interested in finding the shortest-path weights from u to v , which we will denote ( u,v ) . ( u,v ) = if there is no path from u to v in G (Single Source) shortest-path algorithms produce a label: d [ v ] = ( s,v ) . Initially d [ v ] = , reduces as the algorithm goes, so always d [ v ] ( s,v ) Also produce labels [ v ] , predecessor of v on a shortest path from s . Jeff Linderoth IE170:Lecture 21 Shortest Paths The Algorithms Shortest Path Properties Initializing and Relaxing Init-Single-Source ( V,s ) 1 for each v in V 2 do d [ v ] 3 [ v ] nil 4 d [ s ] Relax...
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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