You've learned the basic algorithms now and are ready to step into the area of more complex problems and algorithms to solve them. Advanced algorithms build upon basic ones and use new ideas. We will start with networks flows which are used in more typical applications such as optimal matchings, finding disjoint paths and flight scheduling as well as more surprising ones like image segmentation in computer vision. We then proceed to linear programming with applications in optimizing budget allocation, portfolio optimization, finding the cheapest diet satisfying all requirements and many others. Next we discuss inherently hard problems for which no exact good solutions are known (and not likely to be found) and how to solve them in practice. We finish with a soft introduction to streaming algorithms that are heavily used in Big Data processing. Such algorithms are usually designed to be able to process huge datasets without being able even to store a dataset.

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## 课程信息

### 学生职业成果

## 29%

## 50%

## 25%

### 您将获得的技能

### 学生职业成果

## 29%

## 50%

## 25%

#### 可分享的证书

#### 100% 在线

#### 第 5 门课程（共 6 门）

#### 可灵活调整截止日期

#### 高级

#### 完成时间大约为22 小时

#### 英语（English）

## 教学大纲 - 您将从这门课程中学到什么

**完成时间为 5 小时**

## 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.

**完成时间为 5 小时**

**9 个视频**

**3 个阅读材料**

**1 个练习**

**完成时间为 5 小时**

## 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.

**完成时间为 5 小时**

**10 个视频**

**1 个阅读材料**

**1 个练习**

**完成时间为 5 小时**

## 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.

**完成时间为 5 小时**

**16 个视频**

**2 个阅读材料**

**1 个练习**

**完成时间为 5 小时**

## 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.

**完成时间为 5 小时**

**11 个视频**

**1 个阅读材料**

**1 个练习**

### 审阅

#### 4.6

##### 来自ADVANCED ALGORITHMS AND COMPLEXITY的热门评论

Learned a lot. great material. Tough homework\n\nI appreciated that the grader demanded good implementations but I think it would have been good to have a little guidance as to how to get there.

The problems are really challenging, thank you! However, the instructor is not very active in the discussion forum, which is a pity when you really need help and get stucked in the problem set.

Very Educational and Enlightening. The only criticism I have is that the starter files generally need more modification than indicated to create a successful program.

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!

Very Very Challenging Course , it test your patience and rewards is extremely satisfying. Lot of learning on a complicated subject of NP-Hard problems.

The only thing I missed in this course (and specialization) was more visual, intuitive approach to explanation. Programming assignments are rewarding.

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

Excellent course. One star less just because there are not very clean test cases for one particular problem among programming assignments

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