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.
Este curso forma parte de Programa Especializado - Estructuras de datos y algoritmos
Advanced Algorithms and Complexity
ofrecido por
Universidad de California en San Diego
National Research University Higher School of Economics
Acerca de este Curso
4.5
267 calificaciones
Habilidades que obtendrás
Python ProgrammingLinear Programming (LP)Np-CompletenessDynamic Programming
Programa - Qué aprenderás en este curso
Semana
15 horas para completar
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 videos (Total 72 minutos), 3 readings, 2 quizzes
9 videos
Network Flows9m
Residual Networks10m
Maxflow-Mincut7m
The Ford–Fulkerson Algorithm7m
Slow Example3m
The Edmonds–Karp Algorithm11m
Bipartite Matching11m
Image Segmentation7m
3 lecturas
Slides and Resources on Flows in Networks10m
Available Programming Languages10m
FAQ on Programming Assignments10m
1 ejercicio de práctica
Flow Algorithms10m
Semana
25 horas para completar
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 videos (Total 84 minutos), 1 reading, 2 quizzes
10 videos
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
1 lectura
Slides and Resources on Linear Programming10m
1 ejercicio de práctica
Linear Programming Quiz10m
Semana
35 horas para completar
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 videos (Total 115 minutos), 2 readings, 2 quizzes
16 videos
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
2 lecturas
Slides and Resources on NP-complete Problems10m
Minisat Installation Guide10m
1 ejercicio de práctica
NP-complete Problems12m
Semana
45 horas para completar
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 videos (Total 119 minutos), 1 reading, 2 quizzes
11 videos
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
1 lectura
Slides and Resources on Coping with NP-completeness10m
1 ejercicio de práctica
Coping with NP-completeness6m
40%
comenzó una nueva carrera después de completar estos cursos
57%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
25%
consiguió un aumento de sueldo o ascenso
Principales revisiones
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!
Another great course in this specialization with challenging and interesting assignments. However, this one is somewhat harder but rewarding.
Instructores
Alexander S. Kulikov
Visiting ProfessorDepartment of Computer Science and Engineering
Michael Levin
LecturerComputer Science
Daniel M Kane
Assistant ProfessorDepartment of Computer Science and Engineering / Department of Mathematics
Neil Rhodes
Adjunct FacultyComputer Science and Engineering
Acerca de Universidad de California en San Diego
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.
Acerca de National Research University Higher School of Economics
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
Acerca del programa especializado Estructuras de datos y algoritmos
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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