This course is part of the Data Structures and Algorithms Specialization

Offered By

University of California San Diego

National Research University Higher School of Economics

Data Structures and Algorithms Specialization

University of California San Diego

About this Course

4.5

233 ratings

•

54 reviews

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

Subtitles: English

Python ProgrammingLinear Programming (LP)Np-CompletenessDynamic Programming

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

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

Subtitles: English

Week

1Network 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 videos (Total 72 min), 3 readings, 2 quizzes

Network Flows9m

Residual Networks10m

Maxflow-Mincut7m

The Ford–Fulkerson Algorithm7m

Slow Example3m

The Edmonds–Karp Algorithm11m

Bipartite Matching11m

Image Segmentation7m

Slides and Resources on Flows in Networks10m

Available Programming Languages10m

FAQ on Programming Assignments10m

Flow Algorithms10m

Week

2Linear 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 videos (Total 84 min), 1 reading, 2 quizzes

Linear Programming8m

Linear Algebra: Method of Substitution5m

Linear Algebra: Gaussian Elimination10m

Convexity9m

Duality12m

(Optional) Duality Proofs7m

Linear Programming Formulations8m

The Simplex Algorithm10m

(Optional) The Ellipsoid Algorithm6m

Slides and Resources on Linear Programming10m

Linear Programming Quiz10m

Week

3Although 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 videos (Total 115 min), 1 reading, 2 quizzes

Search Problems9m

Traveling Salesman Problem7m

Hamiltonian Cycle Problem8m

Longest Path Problem1m

Integer Linear Programming Problem3m

Independent Set Problem3m

P and NP4m

Reductions5m

Showing NP-completeness6m

Independent Set to Vertex Cover5m

3-SAT to Independent Set14m

SAT to 3-SAT7m

Circuit SAT to SAT12m

All of NP to Circuit SAT5m

Using SAT-solvers14m

Slides and Resources on NP-complete Problems10m

NP-complete Problems12m

Week

4After 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 videos (Total 119 min), 1 reading, 2 quizzes

2-SAT10m

2-SAT: Algorithm12m

Independent Sets in Trees14m

3-SAT: Backtracking11m

3-SAT: Local Search12m

TSP: Dynamic Programming15m

TSP: Branch and Bound9m

Vertex Cover9m

Metric TSP12m

TSP: Local Search6m

Slides and Resources on Coping with NP-completeness10m

Coping with NP-completeness6m

4.5

54 Reviewsgot a tangible career benefit from this course

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By EM•Jan 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 AS•Jun 15th 2018

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

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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 communications, IT, mathematics, engineering, and more.
Learn more on www.hse.ru...

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....

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Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I subscribe to this Specialization?

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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