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Approximation Algorithms
  • Level Professional
  • المدة 15 ساعات hours
  • الطبع بواسطة EIT Digital
  • Offered by

عن

Many real-world algorithmic problems cannot be solved efficiently using traditional algorithmic tools, for example because the problems are NP-hard. The goal of this course is to become familiar with important algorithmic concepts and techniques needed to effectively deal with such problems. These techniques apply when we don't require the optimal solution to certain problems, but an approximation that is close to the optimal solution. We will see how to efficiently find such approximations. Prerequisites: In order to successfully take this course, you should already have a basic knowledge of algorithms and mathematics. Here's a short list of what you are supposed to know: - O-notation, Ω-notation, Θ-notation; how to analyze algorithms - Basic calculus: manipulating summations, solving recurrences, working with logarithms, etc. - Basic probability theory: events, probability distributions, random variables, expected values etc. - Basic data structures: linked lists, stacks, queues, heaps - (Balanced) binary search trees - Basic sorting algorithms, for example MergeSort, InsertionSort, QuickSort - Graph terminology, representations of graphs (adjacency lists and adjacency matrix), basic graph algorithms (BFS, DFS, topological sort, shortest paths) The material for this course is based on the course notes that can be found under the resources tab. We will not cover everything from the course notes. The course notes are there both for students who did not fully understand the lectures as well as for students who would like to dive deeper into the topics. The video lectures contain a few very minor mistakes. A list of these mistakes can be found under resources (in the document called "Errata"). If you think you found an error, report a problem by clicking the square flag at the bottom of the lecture or quiz where you found the error.

الوحدات

1.1 Introduction

    • 1 Videos
    • 1 Readings
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1 Videos

  • Introduction to Approximation Algorithms

1 Readings

  • Course notes 1.1

Quiz: Introduction

    • 1 Assignment
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1 Assignment

  • Introduction

2.1 A greedy algorithm for load balancing

    • 1 Videos
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1 Videos

  • A greedy algorithm for load balancing

2.2 Analysis of the greedy-algorithm

    • 1 Videos
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1 Videos

  • Analysis of the greedy-algorithm

2.3 The ordered scheduling-algorithm

    • 1 Videos
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1 Videos

  • The ordered scheduling algorithm

2.4 Quiz: The load balancing problem

    • 1 Readings
    • 1 Programming
    • 1 Assignment
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1 Programming

  • Load balancing

1 Assignment

  • The load balancing problem

1 Readings

  • Course notes 1.2

3.1 The vertex cover problem

    • 1 Videos
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1 Videos

  • The vertex-cover problem

3.2 An approximation algorithm for vertex-cover

    • 1 Videos
    • 1 Readings
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1 Videos

  • An approximation algorithm for vertex-cover

1 Readings

  • Course notes 3.1

3.3 A brief introduction to linear programming

    • 1 Videos
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1 Videos

  • A brief introduction to linear programming

3.4 Weighted vertex-cover

    • 1 Videos
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1 Videos

  • Weighted vertex-cover

3.5 LP relaxation for weighted vertex-cover

    • 1 Videos
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1 Videos

  • LP relaxation for weighted vertex-cover

3.6 LP relaxation: Analyzing approximation ratio

    • 1 Videos
    • 1 Readings
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1 Videos

  • LP relaxation: Analyzing approximation ratio

1 Readings

  • Course notes 3.2

3.7 Quiz: LP relaxation

    • 1 Assignment
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1 Assignment

  • LP Relaxation

4.1 Polynomial-time approximation schemes

    • 1 Videos
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1 Videos

  • Polynomial-time approximation schemes

4.2 Knapsack Problem

    • 1 Videos
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1 Videos

  • Knapsack Problem

4.3 A dynamic programming algorithm for knapsack

    • 1 Videos
    • 1 Readings
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1 Videos

  • A dynamic-programming algorithm for knapsack

1 Readings

  • Course notes 4.1

4.4 A PTAS for knapsack

    • 1 Videos
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1 Videos

  • A PTAS for knapsack

4.5 Analysis of the PTAS for knapsack: approximation ratio

    • 1 Videos
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1 Videos

  • Analysis of the PTAS for knapsack: approximation ratio

4.6 Analysis of the PTAS for knapsack: running time

    • 1 Videos
    • 1 Readings
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1 Videos

  • Analysis of the PTAS for knapsack: running time

1 Readings

  • Course notes 4.2

4.7 Quiz: Polynomial-time approximation schemes

    • 1 Programming
    • 1 Assignment
Show info about module content

1 Programming

  • PTAS for load balancing

1 Assignment

  • Polynomial-time approximation schemes

Auto Summary

"Approximation Algorithms" is an advanced course designed for professionals in Data Science & AI, taught by Coursera. It focuses on solving NP-hard problems using algorithmic techniques to find near-optimal solutions efficiently. Learners need a solid foundation in algorithms, mathematics, data structures, and graph theory. The course includes comprehensive video lectures and detailed course notes, spanning 900 minutes. Available under the Starter subscription, it's ideal for those looking to deepen their expertise in algorithmic problem-solving.

Mark de Berg
Instructor

Mark de Berg