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.
Este curso faz parte do Programa de cursos integrados Introduction to Discrete Mathematics for Computer Science
Delivery Problem
oferecido por
Universidade da Califórnia, San Diego
National Research University Higher School of Economics
Programa de cursos integrados Introduction to Discrete Mathematics for Computer ScienceUniversidade da Califórnia, San Diego
Programa - O que você aprenderá com este curso
Semana
14 horas para concluir
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 vídeos (total de (Total 43 mín.) min), 1 leitura, 4 testes
4 videos
Delivery Problem12min
Shortest Common Superstring Problem10min
Brute Force Search11min
Nearest Neighbor8min
1 leituras
Additional Materials10min
4 exercícios práticos
Cycle Weight20min
Brute Force Algorithm2min
Average Weight30min
Nearest Neighbors2min
Semana
24 horas para concluir
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 vídeos (total de (Total 49 mín.) min), 2 testes
4 videos
Branch and Bound14min
Dynamic Programming: Main Ideas9min
Dynamic Programming: Representing Subsets10min
Dynamic Programming: Code13min
2 exercícios práticos
Branch and Bounds
Dynamic Programmings
Semana
34 horas para concluir
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 vídeos (total de (Total 20 mín.) min), 1 teste
1 exercício prático
2-Approximation2min
4.7
9 avaliaçõesMelhores avaliações
This final course in 5 course specialization is relatively easy one, although the last problem takes little bit time to solve. Provides good introduction to difficult to learn Delivery problem.
perfect course! very easy and interesting to follow. Pseudo-Algorithms were very useful and helped a lot to understand the concepts.
Instrutores
Alexander S. Kulikov
Visiting ProfessorDepartment of Computer Science and Engineering
Sobre Universidade da Califórnia, 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.
Sobre 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
Sobre o Programa de cursos integrados Introduction to Discrete Mathematics for Computer Science
Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses.
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