Об этом курсе: We’ll implement (in Python) together efficient programs for a problem needed by delivery companies all over the world millions times per day — the travelling salesman problem. The goal in this problem is to visit all the given places as quickly as possible. How to find an optimal solution to this problem quickly? We still don’t have provably efficient algorithms for this difficult computational problem and this is the essence of the P versus NP problem, the most important open question in Computer Science. Still, we’ll implement several solutions for real world instances of the travelling salesman problem. While designing these solutions, we will rely heavily on the material learned in the courses of the specialization: proof techniques, combinatorics, probability, graph theory. We’ll see several examples of using discrete mathematics ideas to get more and more efficient solutions.
Для кого этот курс: Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Автор: Калифорнийский университет в Сан-Диего, Национальный исследовательский университет "Высшая школа экономики"
Преподаватели: Alexander S. Kulikov, Visiting Professor
Department of Computer Science and Engineering
| Основные сведения | Course 5 of 5 in the Introduction to Discrete Mathematics for Computer Science Specialization |
| Уровень | Beginner |
| Выполнение | 3 weeks of study, 2–5 hours/week |
| Язык | English |
| Как пройти курс | Чтобы пройти курс, выполните все оцениваемые задания. |
| Оценки пользователей |
Программа курса
НЕДЕЛЯ 1
Traveling Salesman Problem
We start this module with the definition of mathematical model of the delivery problem — the classical traveling salesman problem (usually abbreviated as TSP). We'll then review just a few of its many applications: from straightforward ones (delivering goods, planning a trip) to less obvious ones (data storage and compression, genome assembly). After that, we will together take the first steps in implementing programs for TSP.
4 видео, 1 материал для самостоятельного изучения
- Видео: Delivery Problem
- Видео: Shortest Common Superstring Problem
- Leyendo: Additional Materials
- Видео: Brute Force Search
- Видео: Nearest Neighbor
- Libreta: Draw Hamiltonian cycles
- Libreta: Average Weight: Examples
Оцениваемый: Cycle Weight
Оцениваемый: Brute Force Algorithm
Оцениваемый: Average Weight
Оцениваемый: Nearest Neighbors
НЕДЕЛЯ 2
Exact Algorithms
We'll see two general techniques applied to the traveling salesman problem. The first one, branch and bound, is a classical approach in combinatorial optimization that is used for various problems. It can be seen as an improvement of the brute force search: we try to construct a permutation piece by piece, but at each step we check whether it still makes sense to continue constructing the permutation (if it doesn't, we just cut off the current branch). The second one, dynamic programming, is arguably the most popular algorithmic technique. It solves a problem by going through a collection of smaller subproblems.
4 видео, 1 practice quiz
- Видео: Branch and Bound
- Видео: Dynamic Programming: Main Ideas
- Видео: Dynamic Programming: Representing Subsets
- Видео: Dynamic Programming: Code
- Cuestionario de práctica: Dynamic Programming
- Libreta: Integer Linear Programming (Optional)
Оцениваемый: Branch and Bound
НЕДЕЛЯ 3
Approximation Algorithms
As we've seen in the previous modules, solving the traveling salesman problem exactly is hard. In fact, we don't even expect an efficient solution in the nearest future. For this reason, it makes sense to ask: is it possible to find efficiently a solution that is probably suboptimal, but at the same time is close to optimal? It turns out that the answer is yes! We'll learn two algorithms. The first one guarantees to find quickly a solution which is at most twice longer than the optimal one. The second algorithms does not have such guarantees, but it is known to work pretty well in practice.
2 видео
- Видео: Approximation Algorithms
- Видео: Local Search
- Libreta: 2-Approximation. Examples.
Оцениваемый: 2-Approximation
Часто задаваемые вопросы
Как это работает
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Certificados
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Авторы
Калифорнийский университет в Сан-Диего
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.
Национальный исследовательский университет "Высшая школа экономики"
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
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Рейтинги и отзывы
I really enjoyed this course.
This is a nice way to end the course and, seaways nicely into studying algorithms in general.
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Good exercises!