LecX2 - 1 2/11/10 COT 6936 1 COT 6936: Topics in Algorithms...

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Unformatted text preview: 1 2/11/10 COT 6936 1 COT 6936: Topics in Algorithms Giri Narasimhan ECS 254A / EC 2443; Phone: x3748 [email protected] http://www.cs.fiu.edu/~giri/teach/COT6936_S10.html https://online.cis.fiu.edu/portal/course/view.php?id=427 Gaussian Elimination • Solving a system of simultaneous equations x 1-2x 3 = 2 x 2 + x 3 = 3 x 1 + x 2- x 4 = 4 x 2 + 3x 3 + x 4 = 5 x 1-2x 3 = 2 x 2 + x 3 = 3 x 2 + 2x 3- x 4 = 2 x 2 + 3x 3 + x 4 = 5 2/11/10 COT 6936 2 O(n 3 ) algorithm Linear Programming • Want more than solving simultaneous equations • We have an objective function to optimize 2/11/10 COT 6936 3 2 Chocolate Shop [ DPV book ] • 2 kinds of chocolate – milk [Profit: $1 per box] [Demand: 200] – Deluxe [Profit: $6 per box] [Demand: 300] • Production capacity: 400 boxes • Goal: maximize profit – Maximize x 1 + 6x 2 subject to constraints: • x 1 ¡ 200 • x 2 ¡ 300 • x 1 + x 2 ¡ 400 • x 1 , x 2 ¢ 0 2/11/10 COT 6936 4 Diet Problem • Food type : F 1 ,…,F m • Nutrients : N 1 ,…,N n • Min daily requirement of nutrients: c 1 ,…,c n • Price per unit of food: b 1 ,…,b m • Nutrient N j in food F i : a ij • Problem: Supply daily nutrients at minimum cost • Min ¡ i b i x i • ¡ i a ij x i ¢ c j for 1 ¡ j ¡ n • x i ¢ 0 2/11/10 COT 6936 5 Transportation Problem • Ports (Production Units): P 1 ,…,P m • Port/production capacity: s 1 ,…,s m • Markets (Consumption Units): M 1 ,…,M n • Min daily market need: r 1 ,…,r n • Cost of transporting to M k from port P i : a ik • Problem : Meet market need at minimum transportation cost 2/11/10 COT 6936 6 Multicommodity versions 3 Assignment Problem • Workers : b 1 ,…,b n • Jobs : g 1 ,…,g m • Value of assigning person b i to job g k : a ik • Problem : Choose job assignment with maximum value 2/11/10 COT 6936 7 The General Assignment Problem generalizes the Bipartite Matching Problem Bandwidth Allocation Problem 2/11/10 COT 6936 8 • Revenue: A ¡ B pays $3 per unit...
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This note was uploaded on 02/18/2012 for the course CIS 6936 taught by Professor Giri during the Spring '12 term at FIU.

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LecX2 - 1 2/11/10 COT 6936 1 COT 6936: Topics in Algorithms...

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