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Linear programming applications This week we will showcase a few extra surprising applications of linear programming: How to play zero-sum games, and how to ex- ploit the properties of basic solutions to solve discrete optimization problems. 5.1 Playing zero-sum games The easiest way to introduce zero-sum games is to look at a classic game played […]
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Introduction to Discrete Optimization This week we introduce the notion of optimization problems, draw a distinction between continuous and discrete optimization, in- troduce linear programming, and sketch the connection between polyhedral theory and optimization. 1.1 Optimization problems An optimization problem is specified by a set of feasible solutions F and an objective function f :
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Week 2 Simplex Today we will introduce the simplex algorithm for solving a linear programs in standard form1. The main idea behind the algorithm is very simple indeed. It can be distilled into a single sentence: Starting from a basic feasible solution, find an adjacent basic feasible solution with better cost until it is not
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Maximum submodular coverage This week we study the maximum submodular coverage problem, a generalization of the maximum coverage problem. We also intro- duce the concept of approximation algorithms. 11.1 Maximum coverage We start by discussing the maximum coverage problem. Given a collection of subsets S = {S1,…,Sm} of a ground set U, we want to
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Assessed Preparation 1: 2: 3: 4: 5: 6: 7: 8: 9: functionCOUNT(A[1..n],target) count = 0 whilei ≤n do if A[i] = target then count = count + 1 i=i+1 end while return count endfunction Week 2 Studio Sheet (Solutions) Useful advice: The following solutions pertain to the theoretical problems given in the tutorial classes. You
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Week 9 Studio Sheet (Solutions) Useful advice: The following solutions pertain to the theoretical problems given in the tutorial classes. You are strongly advised to attempt the problems thoroughly before looking at these solutions. Simply reading the solu- tions without thinking about the problems will rob you of the practice required to be able to
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Assessed Preparation Week 6 Studio Sheet (Solutions) Useful advice: The following solutions pertain to the theoretical problems given in the tutorial classes. You are strongly advised to attempt the problems thoroughly before looking at these solutions. Simply reading the solu- tions without thinking about the problems will rob you of the practice required to be
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Week 4 Studio Sheet (Solutions) Useful advice: The following solutions pertain to the theoretical problems given in the tutorial classes. You are strongly advised to attempt the problems thoroughly before looking at these solutions. Simply reading the solu- tions without thinking about the problems will rob you of the practice required to be able to
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Implementation checklist Week 10 Studio Sheet (Solutions) Useful advice: The following solutions pertain to the theoretical problems given in the tutorial classes. You are strongly advised to attempt the problems thoroughly before looking at these solutions. Simply reading the solu- tions without thinking about the problems will rob you of the practice required to be
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Assessed Preparation Week 11 Studio Sheet (Solutions) Useful advice: The following solutions pertain to the theoretical problems given in the tutorial classes. You are strongly advised to attempt the problems thoroughly before looking at these solutions. Simply reading the solu- tions without thinking about the problems will rob you of the practice required to be
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