このコースについて
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自分のスケジュールですぐに学習を始めてください。

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約23時間で修了

推奨:4 weeks of study, 4-8 hours/week...

英語

字幕:英語

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Python ProgrammingLinear Programming (LP)Np-CompletenessDynamic Programming

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

上級レベル

約23時間で修了

推奨:4 weeks of study, 4-8 hours/week...

英語

字幕:英語

シラバス - 本コースの学習内容

1
5時間で修了

Flows in Networks

Network flows show up in many real world situations in which a good needs to be transported across a network with limited capacity. You can see it when shipping goods across highways and routing packets across the internet. In this unit, we will discuss the mathematical underpinnings of network flows and some important flow algorithms. We will also give some surprising examples on seemingly unrelated problems that can be solved with our knowledge of network flows.

...
9件のビデオ (合計72分), 3 readings, 2 quizzes
9件のビデオ
Maxflow-Mincut7 分
The Ford–Fulkerson Algorithm7 分
Slow Example3 分
The Edmonds–Karp Algorithm11 分
Bipartite Matching11 分
Image Segmentation7 分
3件の学習用教材
Slides and Resources on Flows in Networks10 分
Available Programming Languages10 分
FAQ on Programming Assignments10 分
1の練習問題
Flow Algorithms10 分
2
5時間で修了

Linear Programming

Linear programming is a very powerful algorithmic tool. Essentially, a linear programming problem asks you to optimize a linear function of real variables constrained by some system of linear inequalities. This is an extremely versatile framework that immediately generalizes flow problems, but can also be used to discuss a wide variety of other problems from optimizing production procedures to finding the cheapest way to attain a healthy diet. Surprisingly, this very general framework admits efficient algorithms. In this unit, we will discuss some of the importance of linear programming problems along with some of the tools used to solve them.

...
10件のビデオ (合計84分), 1 reading, 2 quizzes
10件のビデオ
Linear Algebra: Gaussian Elimination10 分
Convexity9 分
Duality12 分
(Optional) Duality Proofs7 分
Linear Programming Formulations8 分
The Simplex Algorithm10 分
(Optional) The Ellipsoid Algorithm6 分
1件の学習用教材
Slides and Resources on Linear Programming10 分
1の練習問題
Linear Programming Quiz10 分
3
5時間で修了

NP-complete Problems

Although many of the algorithms you've learned so far are applied in practice a lot, it turns out that the world is dominated by real-world problems without a known provably efficient algorithm. Many of these problems can be reduced to one of the classical problems called NP-complete problems which either cannot be solved by a polynomial algorithm or solving any one of them would win you a million dollars (see Millenium Prize Problems) and eternal worldwide fame for solving the main problem of computer science called P vs NP. It's good to know this before trying to solve a problem before the tomorrow's deadline :) Although these problems are very unlikely to be solvable efficiently in the nearest future, people always come up with various workarounds. In this module you will study the classical NP-complete problems and the reductions between them. You will also practice solving large instances of some of these problems despite their hardness using very efficient specialized software based on tons of research in the area of NP-complete problems.

...
16件のビデオ (合計115分), 2 readings, 2 quizzes
16件のビデオ
Hamiltonian Cycle Problem8 分
Longest Path Problem1 分
Integer Linear Programming Problem3 分
Independent Set Problem3 分
P and NP4 分
Reductions5 分
Showing NP-completeness6 分
Independent Set to Vertex Cover5 分
3-SAT to Independent Set14 分
SAT to 3-SAT7 分
Circuit SAT to SAT12 分
All of NP to Circuit SAT5 分
Using SAT-solvers14 分
2件の学習用教材
Slides and Resources on NP-complete Problems10 分
Minisat Installation Guide10 分
1の練習問題
NP-complete Problems12 分
4
5時間で修了

Coping with NP-completeness

After the previous module you might be sad: you've just went through 5 courses in Algorithms only to learn that they are not suitable for most real-world problems. However, don't give up yet! People are creative, and they need to solve these problems anyway, so in practice there are often ways to cope with an NP-complete problem at hand. We first show that some special cases on NP-complete problems can, in fact, be solved in polynomial time. We then consider exact algorithms that find a solution much faster than the brute force algorithm. We conclude with approximation algorithms that work in polynomial time and find a solution that is close to being optimal.

...
11件のビデオ (合計119分), 1 reading, 2 quizzes
11件のビデオ
2-SAT10 分
Independent Sets in Trees14 分
3-SAT: Backtracking11 分
3-SAT: Local Search12 分
TSP: Dynamic Programming15 分
TSP: Branch and Bound9 分
Vertex Cover9 分
Metric TSP12 分
TSP: Local Search6 分
1件の学習用教材
Slides and Resources on Coping with NP-completeness10 分
1の練習問題
Coping with NP-completeness6 分
4.6
69件のレビューChevron Right

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Advanced Algorithms and Complexity からの人気レビュー

by EMJan 4th 2018

As usual, complex arguments explained in simple terms!\n\nSome problems are really tough! (e.g. there's a problem from Google Code Jam).\n\nThank you for this course!

by ASJun 15th 2018

Another great course in this specialization with challenging and interesting assignments. However, this one is somewhat harder but rewarding.

講師

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Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
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Michael Levin

Lecturer
Computer Science
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Daniel M Kane

Assistant Professor
Department of Computer Science and Engineering / Department of Mathematics
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Neil Rhodes

Adjunct Faculty
Computer Science and Engineering

カリフォルニア大学サンディエゴ校について

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory....

ロシア国立研究大学経済高等学院(National Research University Higher School of Economics)について

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

データ構造とアルゴリズムの専門講座について

This specialization is a mix of theory and practice: you will learn algorithmic techniques for solving various computational problems and will implement about 100 algorithmic coding problems in a programming language of your choice. No other online course in Algorithms even comes close to offering you a wealth of programming challenges that you may face at your next job interview. To prepare you, we invested over 3000 hours into designing our challenges as an alternative to multiple choice questions that you usually find in MOOCs. Sorry, we do not believe in multiple choice questions when it comes to learning algorithms...or anything else in computer science! For each algorithm you develop and implement, we designed multiple tests to check its correctness and running time — you will have to debug your programs without even knowing what these tests are! It may sound difficult, but we believe it is the only way to truly understand how the algorithms work and to master the art of programming. The specialization contains two real-world projects: Big Networks and Genome Assembly. You will analyze both road networks and social networks and will learn how to compute the shortest route between New York and San Francisco (1000 times faster than the standard shortest path algorithms!) Afterwards, you will learn how to assemble genomes from millions of short fragments of DNA and how assembly algorithms fuel recent developments in personalized medicine....
データ構造とアルゴリズム

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