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.

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Streaming Algorithms (Optional)

In most previous lectures we were interested in designing algorithms with fast (e.g. small polynomial) runtime, and assumed that the algorithm has random access to its input, which is loaded into memory. In many modern applications in big data analysis, however, the input is so large that it cannot be stored in memory. Instead, the input is presented as a stream of updates, which the algorithm scans while maintaining a small summary of the stream seen so far. This is precisely the setting of the streaming model of computation, which we study in this lecture. The streaming model is well-suited for designing and reasoning about small space algorithms. It has received a lot of attention in the literature, and several powerful algorithmic primitives for computing basic stream statistics in this model have been designed, several of them impacting the practice of big data analysis. In this lecture we will see one such algorithm (CountSketch), a small space algorithm for finding the top k most frequent items in a data stream.