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.

This course is part of the Data Structures and Algorithms Specialization

# Advanced Algorithms and Complexity

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## About this Course

### Learner Career Outcomes

## 29%

## 50%

## 25%

### Skills you will gain

### Learner Career Outcomes

## 29%

## 50%

## 25%

#### Shareable Certificate

#### 100% online

#### Course 5 of 6 in the

#### Flexible deadlines

#### Advanced Level

#### Approx. 22 hours to complete

#### English

## Syllabus - What you will learn from this course

**5 hours to complete**

## 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.

**5 hours to complete**

**9 videos**

**3 readings**

**1 practice exercise**

**5 hours to complete**

## 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.

**5 hours to complete**

**10 videos**

**1 reading**

**1 practice exercise**

**5 hours to complete**

## 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.

**5 hours to complete**

**16 videos**

**2 readings**

**1 practice exercise**

**5 hours to complete**

## 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.

**5 hours to complete**

**11 videos**

**1 reading**

**1 practice exercise**

### Top reviews from Advanced Algorithms and Complexity

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.

### About University of California San Diego

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## About the Data Structures and Algorithms Specialization

## Frequently Asked Questions

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