CO754 Approximation Algorithms in Combinatorial Optimization - Winter 2009


First meeting: Tuesday, Jan. 6, in MC 5158A, 1:00pm

Course Info

This is an introductory, grad level course.

Many of the problems that arise in practical applications of discrete optimization are NP-hard, that is optimal solutions cannot be computed in polynomial-time modulo the P not equal NP conjecture. Current research is focusing on the design of polynomial-time approximation algorithms for such problems. The course will study some of the successful paradigms for designing approximation algorithms and for proving approximation guarantees: the greedy method, formulating and solving LP (linear programming) relaxations, the (LP based) primal-dual method, randomized rounding, semidefinite programming relaxations, approximation of metrics, etc. Some lectures will focus on the hardness of approximating specific problems.
(Similar courses have been offered in Fall'99, Winter'05, and Winter'07, and the plan is to offer this course regularly.)

Time & Place

1:00-2:20pm Tue, Thu, MC 5158A (First meeting: Jan.6 Tuesday)


J.Cheriyan, MC6067, phone: 35591 Office Hours: Tuesdays 3:00-4:00pm


An undergraduate course on the design and analysis of algorithms, including NP-completeness, and an undergraduate course in linear programming.

Grading scheme (Tentative)

Assignments		50%
Project			50%

Texts, Monographs, Lecture Notes, Other Courses

Main Text:
Vijay Vazirani, Approximation Algorithms. ( homepage).

Text on Computational Complexity:
Sanjeev Arora and Boaz Barak, Complexity Theory: A Modern Approach. ( homepage).
PDF files for each chapter and the whole book are on the web; some of the relevant parts are Chapter 2, NP and NP completeness, ( PDF), Chapter 18, PCP and hardness of approximation, ( PDF).

David Williamson, Lecture Notes on Approximation Algorithms, Fall 1998. IBM Research Report RC 21273, February 1999. ( homepage).

Michel Goemans has course notes on randomized algorithms, approximation algorithms, etc. ( homepage).

Cheriyan and Ram Ravi, Lecture Notes on Approximation Algorithms for Network Problems, ( lec notes page).

Hochbaum, D.S. (1996). Approximation algorithms for NP-hard problems. (Boston: PWS publishing co.).

P.Crescenzi, and V.Kann. A compendium of NP optimization problems ( homepage).

David Johnson's NP-Completeness Columns (PDF files for all)

The NP-Completeness Column: The Many Limits on Approximation, David S. Johnson, ACM Transactions on Algorithms (TALG) 2(3):473-489 (July 2006)

Charikar (Princeton), CS 594: Limits on Approximation, S07

Chekuri (UIUC), CS 598: Approximation Algorithms, F06

Gupta & Ravi (CMU), 15-854: Approximation Algorithms, F05

Guruswami & O'Donnell (U.Wash.), CSE 533: The PCP Theorem and Hardness of Approximation, F05

Khot (G.Tech), CS 8002: Probabilistically Checkable Proofs and Hardness of Approximation, F04

Roughgarden (Stanford), CS359: Hardness of Approximation, W07

Salavatipour (UA), CMPUT 675: Topics on Approximation Algorithms and Approximability, F07

Sudan (MIT)

Project Reports by students

Notes have been prepared by the students of the course. Each chapter is based on one or more recent research papers. In most cases, the lectures covered minimal relevant material, so the chapters are based on independent study; the chapters were not scribed from the lectures.


Students are allowed to collaborate on the assignments to the extent of formulating ideas as a group. Each student is expected to write up the solutions by himself or herself. All hints, collaboration, outside help etc. should be explicitly listed in your submission.

Assignment 1, due Jan. 16, 3pm (last update: Jan.5)

Assignment 2, due Jan. 29, 1pm (previous: Jan. 30, 3pm) (last update: Jan.24)

Assignment 3, due Feb. 12, 1pm (last update: Jan.30)

Assignment 4, due Feb. 26, 1pm (last update: Feb.13)

Assignment 5, due Mar. 12, 1pm (last update: Mar.4)

Assignment 6, due Apr. 3, 5pm (last update: Mar.26)

last update of page: Apr 2008