# Approximation Algorithms and Linear Programming

This course, offered by the University of Colorado Boulder, delves into the application of linear and integer programming formulations for solving optimization problems in various domains such as resource allocation, scheduling, and task assignment. It also explores approximation algorithms for NP-hard problems, providing efficient solutions within a constant factor of the optimal solution.

Throughout the course, students will learn to formulate linear and integer programming problems, gain a basic understanding of how they are solved, and comprehend the computation of solutions within an approximation factor of the best possible solutions. The learning experience is supported by instructor-provided notes, readings from textbooks, and assignments that include conceptual multiple-choice questions and problem-solving tasks involving programming and algorithm testing.

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##### Course Modules

This course comprises modules on Linear Programming, Integer Linear Programming, Approximation Algorithms, and the Travelling Salesperson Problem, providing comprehensive insights into solving algorithmic problems.

#### Linear Programming

This module introduces the fundamentals of linear programming, covering topics such as the basics of linear programs, network flow problems, and algorithms for solving linear programs. It also offers interactive notes and a lab session to reinforce the learning.

#### Integer Linear Programming

Explore the concept of integer linear programming in this module, which includes discussions on NP-hardness, vertex cover as an integer linear program, and branch and bound algorithms for solving ILPs. Additionally, there is a tutorial on solving ILPs using Python/PuLP package.

#### Approximation Algorithms : Scheduling, Vertex Cover and MAX-SAT

This module focuses on approximation algorithms for scheduling, vertex cover, and the maximum satisfiability problem. It includes in-depth analyses of job shop scheduling, vertex cover approximation algorithms, and the maximum satisfiability approximation, supported by interactive notes.

#### Travelling Salesperson Problem (TSP) and Approximation Schemes

Delve into the travelling salesperson problem (TSP) and approximation schemes in this module, which explores topics such as NP-hardness, dynamic programming algorithm, metric TSP, and heuristic approaches for TSPs. Interactive notes on TSP basics and exact approaches enhance the learning experience.

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