University of Colorado Boulder
Approximation Algorithms and Linear Programming
University of Colorado Boulder

Approximation Algorithms and Linear Programming

This course is part of Foundations of Data Structures and Algorithms Specialization

Taught in English

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7,685 already enrolled

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Course

Gain insight into a topic and learn the fundamentals

4.9

(19 reviews)

Advanced level

Recommended experience

48 hours (approximately)
Flexible schedule
Learn at your own pace
Progress towards a degree

What you'll learn

  • Formulate linear and integer programming problems for solving commonly encountered optimization problems.

  • Develop a basic understanding of how linear and integer programming problems are solved.

  • Understand how approximation algorithms compute solutions that are guaranteed to be within some constant factor of the optimal solution

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Assessments

18 quizzes, 1 assignment

Course

Gain insight into a topic and learn the fundamentals

4.9

(19 reviews)

Advanced level

Recommended experience

48 hours (approximately)
Flexible schedule
Learn at your own pace
Progress towards a degree

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This course is part of the Foundations of Data Structures and Algorithms Specialization
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There are 4 modules in this course

This module introduces the basics of linear programs and shows how some algorithm problems (such as the network flow problem) can be posed as a linear program. We will provide hands-on tutorials on how to pose and solve a linear programming problem in Python. Finally, we will provide a brief overview of linear programming algorithms including the famous Simplex algorithm for solving linear programs. The problem set will guide you towards posing and solving some interesting problems such as a financial portfolio problem and the optimal transportation problem as linear programs.

What's included

7 videos2 readings5 quizzes1 programming assignment4 ungraded labs

This module will cover integer linear programming and its use in solving NP-hard (combinatorial optimization) problems. We will cover some examples of what integer linear programming is by formulating problems such as Knapsack, Vertex Cover and Graph Coloring. Next, we will study the concept of integrality gap and look at the special case of integrality gap for vertex cover problems. We will conclude with a tutorial on formulating and solving integer linear programs using the python library Pulp.

What's included

6 videos4 quizzes1 assignment1 programming assignment4 ungraded labs

We will introduce approximation algorithms for solving NP-hard problems. These algorithms are fast (often greedy algorithms) that may not produce an optimal solution but guarantees that its solution is not "too far away" from the best possible. We will present some of these algorithms starting from a basic introduction to the concepts involved followed by a series of approximation algorithms for scheduling problems, vertex cover problem and the maximum satisfiability problem.

What's included

5 videos4 quizzes1 programming assignment3 ungraded labs

We will present the travelling salesperson problem (TSP): a very important and widely applicable combinatorial optimization problem, its NP-hardness and the hardness of approximating a general TSP with a constant factor. We present integer linear programming formulation and a simple yet elegant dynamic programming algorithm. We will present a 3/2 factor approximation algorithm by Christofides and discuss some heuristic approaches for solving TSPs. We will conclude by presenting approximation schemes for the knapsack problem.

What's included

11 videos5 quizzes1 programming assignment3 ungraded labs

Instructor

Instructor ratings
4.8 (6 ratings)
Sriram Sankaranarayanan
University of Colorado Boulder
5 Courses54,358 learners

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