**Most recent message posted:
05/06/10.**

- Time and Location: TTh 2:00-3:20, Room SAL 322
- Instructor: David Kempe
- Office hours: by appointment
- There are no TAs.

Many of the most important problems in practice are NP-complete to solve optimally. Thus, it is unlikely that any efficient algorithms exist for solving them. Similarly, even if a problem is solvable in polynomial time, the running time of an optimal algorithm may be prohibitively large for instances of practical importance. In both cases, a well-motivated and common approach is to use "Approximation Algorithms", algorithms which find a valid solution whose quality is guaranteed to be "not too much worse" than the optimal solutions.

The field of Approximation Algorithms has become one of the cornerstones of algorithm design. This course aims to provide a fairly comprehensive introduction to the topic, aimed primarily at students at the graduate level or advanced undergraduates. It covers various design techniques and applications, and also explores the limits of approximability.

The following is a preliminary list of topics that will be covered in terms of techniques. It may be expanded or shortened based on time availability.

- Combinatorial Algorithms
- LP rounding based Algorithms
- Primal-Dual Algorithms
- SDP and Convex Programming based Algorithms
- Approximation Hardness
- metric space embeddings

- CS 570 (grade at least B) or explicit permission of instructor.
- familiarity with mathematical reasoning, in particular probability theory and linear algebra.

- V. Vazirani: Approximation Algorithms (Springer)

In addition, we will occasionally reference recent (and not-so-recent) research or survey papers. Another useful sources of information (in some cases covering material beyond the scope of this course) is the following:

- D. Hochbaum (Ed.): Approximation Algorithms for NP-hard problems (PWS)

- J. Kleinberg and E. Tardos: Algorithm Design (Addison-Wesley).
- T. Cormen, C. Leiserson, R. Rivest and C. Stein: Introduction to Algorithms (MIT Press).

There will be about 4-5 homework assignments, one takehome midterm, and one takehome final. The homeworks will cumulatively count for 40% of the grade, the midterm for 25%, and the final for 35%. All assignments will be posted here once issued.

Homeworks should be predominantly done individually. However, limited interaction is appropriate, so long as it is clearly marked on the homework who you discussed ideas with. The midterm and final must be solved individually.

All students are expected to maintain the utmost level of academic integrity. Passing off anyone else's (whether it be a fellow student or someone outside the university) work as your own is a serious infraction, and will lead to appropriate sanctions. Similarly, any collaboration during exams is prohibited. Please consult the USC Student Conduct Code (general overview) for details on what is and is not appropriate, and for the possible consequences of infractions.

- 05/06/2010: The combined lecture notes for 04/27 and 04/29 have been posted.
- 04/28/2010: The final exam has been posted. It is due in David's office by 5pm on Tuesday, 05/11.
- 04/26/2010: The lecture notes for 04/22 have been posted.
- 04/25/2010: In the final two lectures, we will be covering the paper Local Search Heuristics for k-median and Facility Location Problems by Arya, Garg, Khandekar, Meyerson, Munagala, and Pandit.
- 04/23/2010: The lecture notes for 04/20 have been posted.
- 04/20/2010: The lecture notes for 04/15 have been posted.
- 04/19/2010: The sixth homework assignment has been posted. It is due in class on Thursday, April 29, and cannot be submitted late.
- 04/14/2010: The lecture notes for 04/13 have been posted.
- 04/14/2010: The next few lectures, we will be covering the paper Maximizing a submodular set function subject to a matroid constraint by Calinescu, Chekuri, Pal, and Vondrak.
- 04/08/2010: The due date for the fifth homework has been changed to 04/15.
- 04/05/2010: The fifth homework assignment has been assigned. It consists of Problems 22.6, 22.10, 24.7, 26.12 from the textbook. Homework 5 is due Thursday, April 15, in class.
- 03/29/2010: The fourth homework assignment has been assigned. It consists of Problems 18.6, 19.6, 20.6, 21.4, 21.6 from the textbook. Homework 4 is due Tuesday, April 6, in class.
- 03/09/2010: The midterm exam has been
handed out in class and posted. It is due
**in class**no later than Tuesday, 03/23. - 02/21/2010: The third homework assignment has been assigned. It consists of Problems 12.8, 12.9, 13.4, 14.5 (Hint: Read Section 14.3), 15.5 from the textbook. You may use the following version of 12.7 without proving it: "If the constraint matrix A is totally unimodular, then the extreme point solutions of the fractional LP are integral." Homework 3 is due Tuesday, March 2, in class.
- 02/03/2010: The second homework assignment has been assigned. It consists of Problems 4.2, 5.4, 8.3, 9.9, 11.3 from the textbook. It is due Thursday, February 11, in class.
- 01/20/2010: The first homework assignment has been assigned. It consists of Problems 2.1, 2.13, 2.14, 3.6, 3.8 from the textbook. It is due Thursday, January 28, in class. For Problem 3.6, please keep in mind that it is not appropriate to seek out the reference. Also, for full credit, you need to prove the hint about cycle covers. (Hint for that: Matchings might come in handy.)
- 12/15/2009: This is where you will find all important information and announcements about this class.