Ce cours fait partie de la Spécialisation Introduction to Discrete Mathematics for Computer Science

proposé par

University of California San Diego

National Research University Higher School of Economics

Spécialisation Introduction to Discrete Mathematics for Computer Science

University of California San Diego

À propos de ce cours

4.8

45 notes

•

6 avis

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....

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Recommandé : 3 weeks of study, 2–5 hours/week...

Sous-titres : English...

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Réinitialisez les dates limites selon votre disponibilité.

Recommandé : 3 weeks of study, 2–5 hours/week...

Sous-titres : English...

Week

1We 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 vidéos (Total 43 min), 1 lecture, 4 quiz

Delivery Problem12 min

Shortest Common Superstring Problem10 min

Brute Force Search11 min

Nearest Neighbor8 min

Additional Materials10 min

Cycle Weight20 min

Brute Force Algorithm2 min

Average Weight30 min

Nearest Neighbors2 min

Week

2We'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 vidéos (Total 49 min), 2 quiz

Branch and Bound14 min

Dynamic Programming: Main Ideas9 min

Dynamic Programming: Representing Subsets10 min

Dynamic Programming: Code13 min

Branch and Bound min

Dynamic Programming min

Week

3As 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 vidéos (Total 20 min), 1 quiz

2-Approximation2 min

4.8

par 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.

par 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.

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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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