# Algorithms and Data CS 4800, Spring 2012. Instructor: Karl Lieberherr.

Textbook: Algorithm Design by Jon Kleinberg and Eva Tardos, Pearson and Addison Wesley. 2006, ISBN 0-321-29535-8.

Final Exam 1:00 pm - 3:00 pm F Shillman Hall 420 Apr 20, 2012

## Information about Logic and Games

General Information

### Properties of the Quantifier Game

Engagement and Cooperation with Peers In the playground you play, you get engaged to keep your reputation high. To keep a high reputation you must learn the skills of the domain and apply them in the playground in cooperation with your peers.

Learning by doing You oppose claims made by others and you defend your own claims. This tests your skills in the playground. The quality of your attacks and defences determines your reputation.

The quantifier game is fun. It is hard fun. Even if you play against yourself.

Playing the quantifier game is different than getting together with other students and solving problems. You follow a structured protocol to guide your thinking in the right direction to solve the problem. Once the problem is solved, the quantifier game becomes uninteresting and you stop playing.

The quantifier Game in Action Recipe to teach constructive topic D: Define a playground for D and have the students play. The winning students are teachers and help the other students learn the material through skill demonstrations. The winning students demonstrate superior knowledge in domain D in the context of the given playground. It is important to notice that in order to win in the game you only need clever algorithms. You don't need a proof that they are correct. The text book and lectures will show you how to reason about correctness.

## Course Description

We will study algorithmic problems from conception to implementation, following the text book. The text book says in the Preface: "Algorithmic problems form the heart of computer science but they rarely arrive as cleanly packaged, mathematically precise questions. Rather, they tend to come bundled together with lots of messy, application-specific detail, some of it essential, some of it extraneous. As a result, the algorithmic enterprise consists of two fundamental components: the task of getting to the mathematically clean core of a problem and then the task of identifying the appropriate algorithm design techniques." In this 2012 edition of the course we will practice both components.

Knowledge about algorithm design turns out to be pivotal to your career as some interesting and desirable companies first screen students with algorithm questions before they advance to later stages in the interview process.

We produce an artifact that can solve problems for us and we make predictions about this artifact. The most important prediction is that the algorithm is correct. Often we make predictions about the resource consumption of the algorithm. The time consumed by the algorithm is an important concern, but space and energy could be other resources of interest. The prediction is made over a set of instances, such as all instances of size n. We make other predictions about algorithms: how well they solve problems relative to some standard, like the maximum solution.

## Syllabus

We will basically follow the syllabus sketched on page xx of the text book.

### Week 1

Chapter 1, Preparation for hw 1, working with claims, Gale-Shapley Algorithm, 1.2 Five Representative Problems.

### Week 2

Chapter 2, Basics of Algorithm Analysis, Preparation for the Jar Stress Testing Homework hw2: Chapter 2, exercise 8.

### Week 3

Chapter 3: Graphs, hw3: Jar Stress Testing continued, Topological sorting implementation and systematic optimization.

### Week 4

Chapter 4: Greedy Algorithms.

### Week 5

Chapter 5: Divide and Conquer, Midterm.

### Week 6

Divide and Conquer.

### Week 7

Dynamic Programming

### Week 8

Dynamic Programming

Network Flow

Network Flow

### Week 11

NP and Computational Intractability

### Week 12

Linear Programming, Approximation Algorithms.