CO754 Approximation Algorithms in Combinatorial Optimization - Winter 2008


Prof.Swamy will teach a course in Algorithmic Game Theory in the S08 term, Tue, Thu, 1:00-2:20pm in MC 4060.

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 and Winter'05, and the plan is to offer this course regularly.)

Time & Place

12:30-1:20pm MWF, MC 5045 (First meeting: Jan.7 Monday)


J.Cheriyan, MC6067, phone: 35591 Office Hours: Wednesdays 2:00-3:00pm


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

Grading scheme (Tentative)

Assignments		20%-30%
Scribing lecture notes	30%-40%
Project			30%-40%

Texts, Monographs, Lecture Notes, Other Courses

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).

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

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)


Tentative course outline text


Here are pointers to some relevant papers. Some are references for the lectures.

L.Lovasz, Semidefinite programs and combinatorial optimization, 2000 (postscript, 54 pages)

B.S.Baker, Approximation algorithms for NP-complete problems on planar graphs, J.ACM 1994, 41, 153 - 180

N.Bansal, R.Khandekar, V.Nagarajan, Additive Guarantees for Degree Bounded Direct Network Design (PDF, IBM report). STOC 2008 (to appear).
Also posted on this web page.

H.L.Bodlaender, A.M.C.A.Koster, Combinatorial Optimization on Graphs of Bounded Treewidth, The Computer Journal, July 2007 (survey paper)

B.Chor and Madhu Sudan, A Geometric Approach to Betweenness, SIAM J.DM 11(4) 1998:511-523.

M.X.Goemans, papers on SDPs The original "max cut paper" (with D.P.Williamson) is posted here, as well as two survey papers.

D.E.Knuth, The sandwich theorem (postscript or PDF) Expository notes on Lovasz's theta function.

L.C.Lau, J.Naor, M.R.Salavatipour, M.Singh, Survivable network design with degree or order constraints, STOC 2007.

Williamson's notes on PTAS for Euclidean TSP

Wikipedia entry on Treewidth

"Scribed" notes by students


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 18 Jan. 08 (last update: Jan.10)

Assignment 2, due 1 Feb. 08 (last update: Jan.25)

Assignment 3, due 29 Feb. 08 (last update: Feb.18)

Assignment 4 - Optional, due 11 Apr. 08 (last update: Mar.27)

last update of page: April 2008