CO754 Approximation Algorithms in Combinatorial Optimization - Winter 2012


First meeting: Wednesday, Jan. 4, in MC 5136B, 2:30pm

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.
The plan is to cover a good fraction of Vazirani's book in the lectures, and also to cover some of the more recent results, e.g., from the recent text of Williamson and Shmoys.
(Similar courses have been offered in W'05, W'08, W'09, W'10, W'11.)

Time & Place

2:30-4:20pm Mon, Wed, MC 5136 B (First meeting: Jan.4 Wednesday)


J.Cheriyan, MC6067, phone: 35591 Office Hours: Wednesdays 10:45-11:45am


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%

Lecture Contents (Tentative)

text file

Texts, Monographs, Lecture Notes, Other Courses

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

David Williamson and David Shmoys, The Design of Approximation Algorithms. ( homepage, PDF of book available).

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 (NYU), G22.3033-007: Probabilistically Checkable Proofs and Hardness of Approximation, S08

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

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

Sudan (MIT), Approximability of Optimization Problems, F99

Trevisan (Stanford), CS359G: Graph Partitioning and Expanders, S11

Schedule of talks by class on April 2,3,4, 2012, MC 5th floor. The web-page has links to summaries (4 pages) and to source papers.


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.

Papers and Lecture Notes

Submodular Set Covering (SSC) PDF

Fujito's survey paper, Approximation Algorithms for Submodular Set Cover with Applications, survey, IEICE Trans Inf Syst (2000)

Chernoff Bounds PDF

Garg, Konjevod, Ravi, A polylogarithmic approximation algorithm for the group Steiner tree problem, J.Algorithms (2000)

O(log n/ log log n)-approximation algorithm for ATSP PDF

Asadpour, Goemans, Madry, Oveis Gharan, Saberi An O(log n/ log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem. SODA 2010: 379-389     Also, see Sato's notes/slides from CO754-W2010

Knapsack problem -- DP and FPTAS PDF

PTAS for Euclidean TSP PDF

Sanjeev Arora, Approximation schemes for NP-hard geometric optimization problems: a survey (postscript, author's page) OR Math. Programming B 97, 43--69, 2003, DOI: 10.1007/s10107-003-0438-y (PDF available via UW)

Sebo, Vygen, Shorter Tours by Nicer Ears: 7/5-approximation for graphic TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs (arXiv 2012)        

Simons Foundation, Featured Article Approximately Hard: The Unique Games Conjecture

Trevisan, On Khot's Unique Games Conjecture, Bulletin AMS 49:1, 91-111, 2012

Khot, On The Unique Games Conjecture, 25th Annual IEEE Conference on Computational Complexity (CCC) 2010

Trevisan, Bourgain's embedding of any metric into L1 (CS359G, lec.9)

last update of page: Mar 2012