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 forma parte de Programa Especializado - Introduction to Discrete Mathematics for Computer Science
Delivery Problem
ofrecido por
University of California San Diego
National Research University Higher School of Economics
Programa Especializado - Introduction to Discrete Mathematics for Computer ScienceUniversity of California San Diego
Programa - Qué aprenderás en este curso
Semana
1Traveling 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 videos (Total 43 minutos), 1 reading, 4 quizzes
4 videos
Shortest Common Superstring Problem10m
Brute Force Search11m
Nearest Neighbor8m
1 lectura
Additional Materials10m
4 ejercicios de práctica
Cycle Weight20m
Brute Force Algorithm2m
Average Weight30m
Nearest Neighbors2m
Semana
2Exact 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 videos (Total 49 minutos), 2 quizzes
4 videos
Dynamic Programming: Main Ideas9m
Dynamic Programming: Representing Subsets10m
Dynamic Programming: Code13m
2 ejercicios de práctica
Branch and Bounds
Dynamic Programmings
Semana
3Approximation 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 videos (Total 20 minutos), 1 quiz
1 ejercicio de práctica
2-Approximation2m
4.7
7 revisionesPrincipales revisiones
por AS•Jul 25th 2018
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.
por ES•Jun 19th 2018
perfect course! very easy and interesting to follow. Pseudo-Algorithms were very useful and helped a lot to understand the concepts.
Instructor
Alexander S. Kulikov
Visiting ProfessorDepartment of Computer Science and Engineering
Acerca de University of California 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 communications, IT, mathematics, engineering, and more.
Learn more on www.hse.ru
Acerca del programa especializado 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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