The course covers basic algorithmic techniques and ideas for computational problems arising frequently in practical applications: sorting and searching, divide and conquer, greedy algorithms, dynamic programming. We will learn a lot of theory: how to sort data and how it helps for searching; how to break a large problem into pieces and solve them recursively; when it makes sense to proceed greedily; how dynamic programming is used in genomic studies. You will practice solving computational problems, designing new algorithms, and implementing solutions efficiently (so that they run in less than a second).
Link to work - Algorithm Toolbox
A good algorithm usually comes together with a set of good data structures that allow the algorithm to manipulate the data efficiently. In this course, we consider the common data structures that are used in various computational problems. You will learn how these data structures are implemented in different programming languages and will practice implementing them in our programming assignments. This will help you to understand what is going on inside a particular built-in implementation of a data structure and what to expect from it. You will also learn typical use cases for these data structures.
Link to work - Data Structures
If you have ever used a navigation service to find optimal route and estimate time to destination, you've used algorithms on graphs. Graphs arise in various real-world situations as there are road networks, computer networks and, most recently, social networks! If you're looking for the fastest time to get to work, cheapest way to connect set of computers into a network or efficient algorithm to automatically find communities and opinion leaders in Facebook, you're going to work with graphs and algorithms on graphs.
In this course, you will first learn what a graph is and what are some of the most important properties. Then you'll learn several ways to traverse graphs and how you can do useful things while traversing the graph in some order. We will then talk about shortest paths algorithms — from the basic ones to those which open door for 1000000 times faster algorithms used in Google Maps and other navigational services. You will use these algorithms if you choose to work on our Fast Shortest Routes industrial capstone project. We will finish with minimum spanning trees which are used to plan road, telephone and computer networks and also find applications in clustering and approximate algorithms.
Link to work - Algorithms on Graph
World and internet is full of textual information. We search for information using textual queries, we read websites, books, e-mails. All those are strings from the point of view of computer science. To make sense of all that information and make search efficient, search engines use many string algorithms. Moreover, the emerging field of personalized medicine uses many search algorithms to find disease-causing mutations in the human genome.
You've learned the basic algorithms now and are ready to step into the area of more complex problems and algorithms to solve them. Advanced algorithms build upon basic ones and use new ideas. We will start with networks flows which are used in more typical applications such as optimal matchings, finding disjoint paths and flight scheduling as well as more surprising ones like image segmentation in computer vision. We then proceed to linear programming with applications in optimizing budget allocation, portfolio optimization, finding the cheapest diet satisfying all requirements and many others. Next we discuss inherently hard problems for which no exact good solutions are known (and not likely to be found) and how to solve them in practice. We finish with a soft introduction to streaming algorithms that are heavily used in Big Data processing. Such algorithms are usually designed to be able to process huge datasets without being able even to store a dataset.
In Spring 2011, thousands of people in Germany were hospitalized with a deadly disease that started as food poisoning with bloody diarrhea and often led to kidney failure. It was the beginning of the deadliest outbreak in recent history, caused by a mysterious bacterial strain that we will refer to as E. coli X. Soon, German officials linked the outbreak to a restaurant in Lübeck, where nearly 20% of the patrons had developed bloody diarrhea in a single week. At this point, biologists knew that they were facing a previously unknown pathogen and that traditional methods would not suffice – computational biologists would be needed to assemble and analyze the genome of the newly emerged pathogen. To investigate the evolutionary origin and pathogenic potential of the outbreak strain, researchers started a crowdsourced research program. They released bacterial DNA sequencing data from one of a patient, which elicited a burst of analyses carried out by computational biologists on four continents. They even used GitHub for the project: https://github.com/ehec-outbreak-crowdsourced/BGI-data-analysis/wiki The 2011 German outbreak represented an early example of epidemiologists collaborating with computational biologists to stop an outbreak. In this Genome Assembly Programming Challenge, you will follow in the footsteps of the bioinformaticians investigating the outbreak by developing a program to assemble the genome of the E. coli X from millions of overlapping substrings of the E.coli X genome.