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Approximation Algorithms and Linear Programming · LearnSpace
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Approximation Algorithms and Linear Programming

Курс от University of Colorado Boulder
Продвинутый≈ 46.3 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course continues our data structures and algorithms specialization by focussing on the use of linear and integer programming formulations for solving algorithmic problems that seek optimal solutions to problems arising from domains such as resource allocation, scheduling, task assignment, and variants of the traveling salesperson problem. Next, we will study algorithms for NP-hard problems whose solutions are guaranteed to be within some approximation factor of the best possible solutions. Such algorithms are often quite efficient and provide useful bounds on the optimal solutions. The learning will be supported by instructor provided notes, readings from textbooks and assignments. Assignments will include conceptual multiple-choice questions as well as problem solving assignments that will involve programming and testing algorithms. This course can be taken for academic credit as part of CU Boulder’s Masters of Science in Computer Science (MS-CS) degrees offered on the Coursera platform. This fully accredited graduate degree offer targeted courses, short 8-week sessions, and pay-as-you-go tuition. Admission is based on performance in three preliminary courses, not academic history. CU degrees on Coursera are ideal for recent graduates or working professionals. Learn more: MS in Computer Science: https://coursera.org/degrees/ms-computer-science-boulder

Навыки, которые вы освоите

AlgorithmsPython ProgrammingTheoretical Computer ScienceCombinatoricsOperations ResearchMathematical ModelingGraph TheoryNetwork ModelMathematical SoftwareModel Optimization

Программа курса

4 модулей · 72 учебных материалов

01Linear Programming23 материалов

Course Introduction

Course Updates and Accessibility SupportЧтениеEarn Academic Credit for your Work!ЧтениеCourse SupportЧтениеAssessment ExpectationsЧтение

Учитесь у экспертов

Sriram Sankaranarayanan

Professor

Approximation Algorithms and Linear Programming
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Обучение откроется на Coursera
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Обучение на Coursera

≈ 46.3 ч

4 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Узбекский, Китайский (Китай), Бразильский португальский, Вьетнамский, Немецкий, Пушту, Урду, Русский, Индонезийский, Азербайджанский, Испанский, Дари, Хинди, Казахский, Венгерский

Часть программы вашего университета
AI Citation and AcknowledgementЧтение

What is a Linear Program?

Introduction to Linear ProgrammingВидеоWhat is a Linear Program?ВидеоExample: Cake-Sharing ProblemВидеоSolving Linear ProgramsВидеоInteractive Notes: Basics of Linear ProgramsЛабораторнаяAI Policy QuizЗаданиеBasics of Linear ProgramsЗадание

Tutorial: Solving Linear Programs Using PuLP Library

Lab: Formulate and Solve LPs using PULPЛабораторнаяSolving LPs using PULPЗадание

Network Flow Problems and Linear Programming

Network Flow Problems and Linear ProgramsВидеоInteractive Notes: Diet Problem and Network Flow ProblemsЛабораторнаяNetwork Flow Problems as LPsЗадание

Geometry of Linear Programs

Geometry of Linear ProgramsВидеоGeometry of Linear ProgramsЗадание

Algorithms for Linear Programs: A brief overview

Algorithms for Solving Linear ProgramsВидеоInteractive Notes on Geometry of Linear Programs and Simplex AlgorithmЛабораторнаяLP AlgorithmsЗадание

Problem Set # 1

Linear ProgrammingПрограммирование
02Integer Linear Programming16 материалов

What is an Integer Linear Program?

What is an Integer Linear Program?ВидеоFormal Introduction to Integer Linear ProgramsВидео

NP-Hardness of Integer Linear Programs

NP Hardness of Integer Linear ProgrammingВидеоInteger Linear ProgrammingЗадание

Tutorial: Solving Integer Linear Programs using Python/Pulp

Tutorial on solving ILPs using Python/PuLP packageЛабораторнаяFormulating/Solving ILPs Задание

Vertex Cover as Integer Linear Program

Vertex Cover as an Integer Linear ProgramВидеоInteractive Notes: Vertex Cover as an ILPЛабораторнаяVertex Cover Problem ILP formulationЗадание

Linear Programming Approximations of Vertex Cover

Linear Programming Approximations to Vertex CoverВидеоInteractive Notes: Integrality Gap for Vertex CoverЛабораторнаяVertex Cover ILP, LP Relaxation and Integrality Gap.Задание

Solving Integer Linear Programs using Branch and Bound Algorithm

Branch and Bound Algorithm for Solving Integer Linear ProgramsВидеоInteractive Notes: Branch and Bound Solvers for ILPsЛабораторнаяBranch and Bound SolversЗадание

Problem Set # 2

Integer Linear ProgramsПрограммирование
03Approximation Algorithms : Scheduling, Vertex Cover and MAX-SAT13 материалов

Approximation Algorithms and Approximation Ratios: Introduction

Introduction to Approximation AlgorithmsВидеоApproximation Algorithm BasicsЗадание

Jobshop Minimum Makespan Scheduling

Introduction to Jobshop Scheduling and Algorithm DesignВидеоAnalysis of Jobshop SchedulingВидеоInteractive Notes: Jobshop SchedulingЛабораторнаяJob Shop Scheduling QuestionsЗадание

Vertex Cover

Approximation Algorithms for Vertex Cover and their AnalysisВидеоInteractive Notes on Vertex Cover Approximation AlgorithmsЛабораторнаяVertex CoverЗадание

Maximum Satisfiability Problem

Approximation Algorithms for the Maximum Satisfiability Problem ВидеоInteractive Notes on Maximum Satisfiability ApproximationЛабораторнаяMax-SAT ApproximationЗадание

Problem Set # 3

Approximation AlgorithmsПрограммирование
04Travelling Salesperson Problem (TSP) and Approximation Schemes20 материалов

Travelling Salesperson Problem (TSP)

Introduction to TSP and its applicationsВидеоNP-Hardness of TSPsВидеоHardness of Approximating General TSPsВидеоInteractive Notes on TSP Basics, NP-Hardness and InapproximabilityЛабораторнаяTSP BasicsЗадание

Exact Algorithms for TSP

Held and Karp's Dynamic Programming AlgorithmВидеоInteger Linear Programming FormulationВидеоSubtours and Subtour Elimination FormulationВидеоInteractive Notes on Exact Approaches to TSPЛабораторнаяHeld-Karp AlgorithmЗаданиеTSP Integer ProgrammingЗадание

Approximation Algorithm for TSP

Metric TSP and ShortcuttingВидеоEulerian Walks for approximating TSPsВидеоChristofides Algorithm and its AnalysisВидеоInteractive Notes: Approximations for Metric TSPsЛабораторнаяApproximations for Metric TSPsЗадание

Heuristics: A Brief Tour

Heuristics for TSPsВидео

Approximation Schemes and the Knapsack Problem

Full Polynomial Time Approximation Scheme and KnapsackВидеоFully Polynomial Time Approximation SchemeЗадание

Problem Set # 4

Travelling Salesperson Problems (TSP)Программирование