lecture17 - CS 473: Algorithms Chandra Chekuri...

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Unformatted text preview: CS 473: Algorithms Chandra Chekuri chekuri@cs.illinois.edu 3228 Siebel Center University of Illinois, Urbana-Champaign Fall 2009 Chekuri CS473ug Introduction Solving Linear Programs Duality Integer Linear Programming Part I Introduction to Linear Programming Chekuri CS473ug Introduction Solving Linear Programs Duality Integer Linear Programming Examples General Form Cannonical Forms History Maximum Flow in Network s 1 2 3 4 5 6 t 15 5 10 30 8 4 9 4 15 6 10 10 15 15 10 Chekuri CS473ug Introduction Solving Linear Programs Duality Integer Linear Programming Examples General Form Cannonical Forms History Maximum Flow in Network s 1 2 3 4 5 6 t 15 5 10 30 8 4 9 4 15 6 10 10 15 15 10 Need to compute values f s 1 , f s 2 ,... f 25 ,... f 5 t , f 6 t such that Chekuri CS473ug Introduction Solving Linear Programs Duality Integer Linear Programming Examples General Form Cannonical Forms History Maximum Flow in Network s 1 2 3 4 5 6 t 15 5 10 30 8 4 9 4 15 6 10 10 15 15 10 Need to compute values f s 1 , f s 2 ,... f 25 ,... f 5 t , f 6 t such that f s 1 15 f s 2 5 f s 3 10 f 14 30 f 21 4 f 25 8 f 32 4 f 35 15 f 36 9 f 42 6 f 4 t 10 f 54 15 f 5 t 10 f 65 15 f 6 t 10 Chekuri CS473ug Introduction Solving Linear Programs Duality Integer Linear Programming Examples General Form Cannonical Forms History Maximum Flow in Network s 1 2 3 4 5 6 t 15 5 10 30 8 4 9 4 15 6 10 10 15 15 10 Need to compute values f s 1 , f s 2 ,... f 25 ,... f 5 t , f 6 t such that f s 1 15 f s 2 5 f s 3 10 f 14 30 f 21 4 f 25 8 f 32 4 f 35 15 f 36 9 f 42 6 f 4 t 10 f 54 15 f 5 t 10 f 65 15 f 6 t 10 and f s 1 + f 21 = f 14 f s 2 + f 32 = f 21 + f 25 f s 3 = f 32 + f 35 + f 36 f 14 + f 54 = f 42 + f 4 t f 25 + f 35 + f 65 = f 54 + f 5 t f 36 = f 65 + f 6 t Chekuri CS473ug Introduction Solving Linear Programs Duality Integer Linear Programming Examples General Form Cannonical Forms History Maximum Flow in Network s 1 2 3 4 5 6 t 15 5 10 30 8 4 9 4 15 6 10 10 15 15 10 Need to compute values f s 1 , f s 2 ,... f 25 ,... f 5 t , f 6 t such that f s 1 15 f s 2 5 f s 3 10 f 14 30 f 21 4 f 25 8 f 32 4 f 35 15 f 36 9 f 42 6 f 4 t 10 f 54 15 f 5 t 10 f 65 15 f 6 t 10 and f s 1 + f 21 = f 14 f s 2 + f 32 = f 21 + f 25 f s 3 = f 32 + f 35 + f 36 f 14 + f 54 = f 42 + f 4 t f 25 + f 35 + f 65 = f 54 + f 5 t f 36 = f 65 + f 6 t f s 1 f s 2 f s 3 f 4 t f 5 t f 6 t Chekuri CS473ug Introduction Solving Linear Programs Duality Integer Linear Programming Examples General Form Cannonical Forms History Maximum Flow in Network s 1 2 3 4 5 6 t 15 5 10 30 8 4 9 4 15 6 10 10 15 15 10 Need to compute values f s 1 , f s 2 ,... f 25 ,... f 5 t , f 6 t such that f s 1 15 f s 2 5 f s 3 10 f 14 30 f 21 4 f 25 8 f 32 4 f 35 15 f 36 9 f 42 6 f 4 t 10 f 54 15 f 5 t 10...
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This note was uploaded on 01/22/2012 for the course CS 573 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.

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lecture17 - CS 473: Algorithms Chandra Chekuri...

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