COS 521: A Graduate Course in Algorithm Design and Analysis

These are lecture notes from a graduate course for Computer Science graduate students at Princeton University in Fall 2013 and Fall 2014. (The course also attracts undergrads and non-CS grads and total enrollment in 2014 was 35.) The course assumes prior knowledge of algorithms at the undergraduate level. This new course arose out of thinking about the right algorithms training for CS grads today, since the environment for algorithms design and use has greatly changed since the 1980s when the canonical grad algorithms courses were designed. The course topics are somewhat nontraditional, and some of the homeworks involve simple programming assignments that encourage students to play with algorithms using simple environments like Matlab and Scipy. Since this is the last theory course many of my students (grad or undergrad) might take for the rest of their lives, I think of the scope as more than just algorithms; my goal is to make them look at the world anew with a mathematical/algorithmic eye. For instance, I discovered many holes in my students’ undergraduate CS education: information/coding theory, economic utility and game theory, decision-making under uncertainty, cryptography (anything beyond the RSA cryptosystem), etc. So I created space for these topics as well, figuring that the value added by this was greater than by, say, presenting detailed analysis of the Ellipsoid algorithm (which I sketch instead). Programming assignments went out of fashion in most algorithms courses in the past few decades, but I think it is time to bring them back. First, CS students are used to a hands-on learning experience; an algorithm becomes real only once they see it run on real data. Second, the computer science world increasingly relies on off-the-shelf packages and library routines, and this is how algorithms are implemented in industry. One can write a few lines of code in matlab and scipy, and run it within minutes on datasets of millions or billions of numbers. No JAVA or C++ needed! Algorithms education should give students at least a taste of such powerful tools. Finally, even for theory students it can be very beneficial to play with algorithms and data a bit; this will help them develop a different kind of theory. The course gives students a choice between taking a 48-hour final, or doing a collaborative term project. Some sample term projects can be found at the course home page. http://www.cs.princeton.edu/courses/archive/fall14/cos521/ This course is very much a work in progress, and I welcome your feedback and suggestions. I thank numerous colleagues for useful suggestions during the design of this course. Above all, I thank my students for motivating me to teach them better; their feedback and questions have helped shape these course notes. Sanjeev Arora March 2015