Combinatorial Optimization: Exact and Approximate Algorithms

In this course we study algorithms for combinatorial optimization problems. Those are the type of algorithms that arise in countless applications, from billion-dollar operations to everyday computing task; they are used by airline companies to schedule and price their flights, by large companies to decide what and where to stock in their warehouses, by delivery companies to decide the routes of their delivery trucks, by Netflix to decide which movies to recommend you, by a gps navigator to come up with driving directions and by word-processors to decide where to introduce blank spaces to justify (align on both sides) a paragraph. 

In this course we will focus on general and powerful algorithmic techniques, and we will apply them, for the most part, to highly idealized model problems. 

Some of the problems that we will study, along with several problems arising in practice, are NP-hard, and so it is unlikely that we can design exact efficient algorithms for them. For such problems, we will study algorithms that are worst-case efficient, but that output solutions that can be sub-optimal. We will be able, however, to prove worst-case bounds to the ratio between the cost of optimal solutions and the cost of the solutions provided by our algorithms. Sub-optimal algorithms with provable guarantees about the quality of their output solutions are called approximation algorithms.