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
oferecido por
Programa de cursos integrados Introduction to Discrete Mathematics for Computer ScienceUniversidade da Califórnia, San DiegoInformações sobre o curso
oferecido por
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.
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.
Programa - O que você aprenderá com este curso
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.
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.
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.
Avaliações
Principais avaliações do DELIVERY PROBLEM
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.
This is a very nice course. I feel that a further explanation in the coding problems would be useful since sometimes you are not sure what one should return from the function.
A fun conclusion to the specialization that brings all of the mathematics of combinatorics and graph theory together to show how it can be applied to some real world problems.
Well structured introductory course into transportation problems. The code in examples is well written and clean. It was a pleasure to study this course.
Sobre Programa de cursos integrados Introduction to Discrete Mathematics for Computer Science
Perguntas Frequentes – FAQ
Quando terei acesso às palestras e às tarefas?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
- The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
- The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
O que recebo ao me inscrever nesta Especialização?
Quando você se inscreve no curso, tem acesso a todos os cursos na Especialização e pode obter um certificado quando concluir o trabalho. Seu Certificado eletrônico será adicionado à sua página de Participações e você poderá imprimi-lo ou adicioná-lo ao seu perfil no LinkedIn. Se quiser apenas ler e assistir o conteúdo do curso, você poderá frequentá-lo como ouvinte sem custo.
Qual é a política de reembolso?
Se você se inscrever, terá 7 dias para testar sem custo e, durante este período, pode cancelar sem multa. Depois disso, não reembolsamos, mas você pode cancelar sua inscrição a qualquer momento. Veja nossa política para o reembolso total.
Existe algum auxílio financeiro disponível?
Sim, a Coursera oferece auxílio financeiro ao aluno que não possa pagar a taxa. Faça a solicitação clicando no link Auxílio Financeiro, abaixo do botão "Inscreva-se" à esquerda. Preencha uma solicitação e será notificado caso seja aprovado. Você terá que completar esta etapa para cada curso na Especialização, incluindo o Trabalho de Conclusão de Curso. Saiba mais .
Mais dúvidas? Visite o Central de Ajuda ao Aprendiz.
