Administrative Stuff

• TA for the course is TBD. (tbd@cs.ucsb.edu)
• TA Hours: TBD.
• TA Location: TBD.

Course Description

Algorithmic thinking is at the heart of computer science. Whether we are concerned with sending messages in the Internet, understanding the structure of a social network, indexing the web graph for key word searches, or auctioning the wireless spectrum, the underlying core problem is often an algorithmic one. The problems, however, rarely come as cleanly packaged, mathematically precise questions, and so the algorithmic enterprise necessarily consists of first getting to the mathematical core of a problem, and then identifying the appropriate algorithm design technique.

The goal of this course is to expose students to this process using a variety of topics and techniques. The general theme of the course is combinatorial algorithms, which can be described loosely as those dealing with discrete structures such as graphs and networks. The course is structured around a loosely related set of techniques and topics that I consider both fundamental and great examples of theoretical elegance.

The following is a tentative list of topics I plan to cover. Some of these are based on research papers of the past decade, and you are strongly encouraged to study them.

Syllabus

Small World Phenomena

An Algorithmic Perspective. Models of Internet connectivity.

6 degrees of separation. Upper and lower bound theorems.

Reading List:

The small-world phenomenon: An algorithmic perspective, by Jon Kleinberg.

The diameter of the world wide web, by Albert, Jeong, Barabasi.

Theory of Network Flows

Flow Networks. Maxflow-Mincut theorem.

Ford-Fulkerson Scheme. Polynomial Schemes for maxflow.

Disjoint paths, other applications, and extensions.

Reading List:

Network Flows: Theory, Algorithms, and Applications, by Ahuja, Magnanti, Orlin.

Introduction to Algorithms, by Cormen, Leiserson, Rivest, Stein.

Algorithm Design, Kleinberg and Tardos.

Network Monitoring

Distributed monitoring. Epsilon-Cut Guarantees.

VC Dimension and Small Detection Sets.

Reading List:

Detecting a Network Failure. Jon Kleinberg, in Internet Mathematics, 2003.

The Probabilistic Method, Noga Alon and Joel Spencer.

Economics and Computer Science

Social choice, voting and Arrow's Theorem.

Combinatorial Auctions.

Reading List:

Introduction to Mechanism Design (for Computer Scientists), by Nisan. Available at http://www.cs.huji.ac.il/~noam/mkts.html.

Roughgarden Lecture Notes on Combinatorial Auctions. Available at http://theory.stanford.edu/~tim/f05/ca.ps

Optimization with Linear Constraints

Linear Programming Formulation.

Simplex Method. Primal-Dual Theorem.

Integer-linear programming.

Reading List:

Linear Programming, V. Chvatal.

Data Streams: Computing in one-pass

Estimating distinct elements.

Estimating frequency moments, quantiles.

Reading List:

The space complexity of approximating the frequenceyu moments, by Alon, Matias, Szegedy.

Data Streams: Algorithms and Applications, by Muthukrishnan

Organization

• This is a theoretical, lecture-based course. There is no single textbook, and the material is compiled for several books and research papers. The course web site lists the main resources. For most of the lectures, I will post below plain ascii lecture notes, but they are unpolished---no figures, no fancy formatting---meant to help organize my own thoughts.

Lecture Notes

• Small World Phenomenon
• Network Flows
• Extensions, Min cost flow
• Detecting Network Failures
• Proof of epsilon net theorem
• Algorithmic Game Theory
• Network Formation: Anarchy, Stability
• 3 Brief Proofs of Arrow's Impossibility Theorem
• Another Graphical Proof Of Arrow's Impossibility Theorem

Grading and Policies

• The course grade will be based on weekly quizzes and a final exam.