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.
제공자:
이 강좌에 대하여
제공자:
캘리포니아 샌디에고 대학교
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.
국립 연구 고등 경제 대학
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.
강의 계획 - 이 강좌에서 배울 내용
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.
검토
DELIVERY PROBLEM의 최상위 리뷰
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.
Introduction to Discrete Mathematics for Computer Science 특화 과정 정보
Discrete Mathematics is the language of Computer Science. One needs to be fluent in it to work in many fields including data science, machine learning, and software engineering (it is not a coincidence that math puzzles are often used for interviews). We introduce you to this language through a fun try-this-before-we-explain-everything approach: first you solve many interactive puzzles that are carefully designed specifically for this online specialization, and then we explain how to solve the puzzles, and introduce important ideas along the way. We believe that this way, you will get a deeper understanding and will better appreciate the beauty of the underlying ideas (not to mention the self confidence that you gain if you invent these ideas on your own!). To bring your experience closer to IT-applications, we incorporate programming examples, problems, and projects in the specialization.
자주 묻는 질문
강의 및 과제를 언제 이용할 수 있게 되나요?
강의 및 과제 이용 권한은 등록 유형에 따라 다릅니다. 청강 모드로 강좌를 수강하면 대부분의 강좌 자료를 무료로 볼 수 있습니다. 채점된 과제를 이용하고 수료증을 받으려면 청강 도중 또는 이후에 수료증 경험을 구매해야 합니다. 청강 옵션이 표시되지 않는 경우:
- 강좌에서 청강 옵션을 제공하지 않을 수 있습니다. 대신 무료 평가판을 사용하거나 재정 지원을 신청할 수 있습니다.
이 전문 분야를 구독하면 무엇을 이용할 수 있나요?
강좌를 등록하면 전문 분야의 모든 강좌에 접근할 수 있고 강좌를 완료하면 수료증을 취득할 수 있습니다. 전자 수료증이 성취도 페이지에 추가되며 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 내용만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.
Is financial aid available?
예, Coursera에서는 수업료를 낼 수 없는 학습자를 위해 재정 지원을 제공합니다. 왼쪽에 있는 등록 버튼 아래 재정 지원 링크를 클릭하면 지원할 수 있습니다. 신청서를 작성하라는 메시지가 표시되며 승인되면 알림을 받습니다. 성취 프로젝트를 포함하여 전문 분야의 각 강좌에서 이 단계를 완료해야 합니다. 자세히 알아보기.
궁금한 점이 더 있으신가요? 학습자 도움말 센터를 방문해 보세요.
