Week 1 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 […]
Week 8 Large Scale Optimization We have seen a few examples of linear programs that are exponen- tially large on the size of the input of problem they are supposed to be modeling. This week we see some techniques to handle lin- ear program with a large number of constraints or variables. We will also
Week 0 Background material This unit of study assumes some basic knowledge of discrete math- ematics, algorithm analysis, and linear algebra. This is all basic material that you should have learned in other units of study. This note is only meant to serve as a quick review of some key concepts and notation that we
Discussion 8 1. You have successfully computed a maximum s-t flow f for a network G = (V; E) with integer edge capacities. Your boss now gives you another network G’ that is identical to G except that the capacity of exactly one edge is decreased by one. You are also explicitly given the edge
fx Y X Xm LY Yul Say M is either an opt solution XmYn EM or 0PTC XmYn M Define Discussion 7 1. When their respective sport is not in season, USC’s student-athletes are very involved in their community, helping people and spreading goodwill for the school. Unfortunately, NCAA regulations limit each student-athlete to at
THE UNIVERSITY OF NEW SOUTH WALES 10. LINEAR PROGRAMMING Raveen de Silva, office: K17 202 Course Admin: , School of Computer Science and Engineering UNSW Sydney Term 3, 2021 Table of Contents 1. Example Problems 2. Linear Programming 3. Puzzle Linear Programming problems: Example 1 Problem Instance: a list of food sources F1, . .
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THE UNIVERSITY OF NEW SOUTH WALES 11. INTRACTABILITY Raveen de Silva, office: K17 202 Course Admin: , School of Computer Science and Engineering UNSW Sydney Term 3, 2021 Table of Contents 1. Feasibility of Algorithms 2. Polynomial Reductions 3. Optimisation Problems 4. Puzzle Polynomial Time Algorithms Definition A (sequential) algorithm is said to be polynomial
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THE UNIVERSITY OF NEW SOUTH WALES 4. INTEGER MULTIPLICATION II Raveen de Silva, office: K17 202 Course Admin: , School of Computer Science and Engineering UNSW Sydney Term 3, 2021 Table of Contents 1. Recap 2. ’s algorithm 3. Puzzle Basics revisited: how do we multiply two numbers? The primary school algorithm: X X X
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CS570 Spring 2018: Analysis of Algorithms Exam III Points 15 10 10 Points 20 Problem 5 15 Problem 6 15 Problem 7 Problem 1 Problem 2 Problem 3 Problem 4 15 Total: 100 Points Instructions: 1. This is a 2-hr exam. Closed book and notes 2. If a description to an algorithm or a proof
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THE UNIVERSITY OF NEW SOUTH WALES 3. INTEGER MULTIPLICATION I Raveen de Silva, office: K17 202 Course Admin: , School of Computer Science and Engineering UNSW Sydney Term 3, 2021 Table of Contents 1. Master Theorem 1.1 Statement 1.2 Examples 1.3 Proof 2. Arithmetic Operations 2.1 Applying D&C to multiplication of large integers 2.2 The
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