Note: webpage still under construction.

CSE 704/711: LP/SDP-Based Approximation Algorithms


Hung Ngo
Hung Ngo's Email Address
(716) 645-3180 x 160
238 Bell Hall


Atri Rudra
Atri's Email Address
(716) 645-3180 x 117
123 Bell Hall

Class Meetings


Brief Description

There are four basic components in this seminar:
These have become standard tools for algorithmists. In fact, they should become part of your toolkit no matter which area of computer science you work on, as optimization problems and their solutions are extremely pervasive.


Course Blog

We will be using a blog for the course in lieu of a course newsgroup. All announcements will be made on the blog. If you are attending the course, you must check the blog regularly (and consider subscribing to the RSS feed).

Reference materials

We will not follow any particular textbook. We will mostly follow papers. Here are some resources relevant to the seminar.

Tentative Schedule

Dates Topic Lecturer
Week 1, Mon Aug 31 Intro to Linear Programming & Approximation algorithms Atri Rudra
Week 1, Wed Sep 02 Duality, Complementary Slackness, Farkas Lemma
Week 2, Mon Sep 07 Labor day! Hung Ngo
Week 2,  An overview of approximation algorithm design via Vertex Cover; a little more on LP and characterization of extreme point solutions. Half-integrality of vertex cover. How to take the dual program.
Week 3, Mon Sep 14 LP/ILP and total unimodularity. Maxflow/mincut.
Week 3,  Total unimodularity. Ellipsoid method, separation oracle
Week 4, Mon Sep 21 Rounding and randomized rounding. Examples: cut problems, covering problems, satisfiability problems.
Week 4, Wed Sep 23 Iterative rounding
Week 5, Mon Sep 28 Yom Kippur!
Week 5,  Iterative rounding
Week 6, Mon Oct 05 Primal-dual
Week 6,  Primal-dual
Week 7, Mon Oct 12 Primal-Dual. (Swamy's paper, maybe.)
Week 7,  More sophisticated rounding techniques. Metric embedding
Week 8, Mon Oct 19 Steve Uutarmo: Anupam Gupta & Kunal Talwar, Approximating Unique Games, SODA 2006.
Swapnoneel Roy: L. Lau, M. Singh. Approximating Minimum Bounded Degree Spanning Trees to within One of Optimal. STOC 2007.
Student Presentations
Week 8,  Lei Xu: Robert D. Carr, Santosh Vempala: Randomized metarounding. Random Struct. Algorithms 20(3): 343-352 (2002). (also appeared in STOC'00)
Branislav Stojkovic: Jain and Vazirani, Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. ACM 48, 2, 274–296, 2001.
Week 9, Mon Oct 26 Xi Wan: Dorit Hochbaum, N. Megiddo, J. Naor and A. Tamir "Tight Bounds and 2-approximation Algorithms for Integer Programs with Two Variables Per Inequality," Mathematical Programming, 62 (1993)

Week 9 Krishna Ramkumar: Bansal, N., Khandekar, R., and Nagarajan, V. 2008. Additive guarantees for degree bounded directed network design. STOC 2008.
Arun Ramachandramurthy: Cheung & Swamy, Approximation Algorithms for Single-minded Envy-free Profit-maximization Problems with Limited Supply, Proceedings of FOCS 2008, pages 35-44.
Week 10, Mon Nov 02 Thanh-Nhan Nguyen: L. Lau, M. Singh Additive Approximation for Bounded Degree Survivable Network Design. STOC 2008
Nathan Russell: Lavi & Swamy, Truthful and Near-optimal Mechanism Design via Linear Programming, Proceedings of FOCS 2005, pages 595-604.
Week 10, Wed Atri Rudra
Week 11, Mon Nov 09
Week 11, Wed
Week 12, Mon Nov 16
Week 12, Wed
Week 13, Mon Nov 23 Thanh-Nhan Nguyen:"Primal dual algorithms for SDPs: A combinatorial, primal-dual approach to solving SDPs". Sanjeev Arora, Satyen Kale. Proc. ACM STOC 2007.
Nathan Russell: "Near-Optimal Algorithms for Unique Games," Moses Charikar, Konstantin Makarychev, Yury Makarychev, STOC 2006
Student Presentations
Week 13, Wed Fall Recess!
Week 14, Mon Nov 30 Krishna Ramkumar: Raghavendra Prasad. *Optimal Algorithms and Inapproximability Results for Every CSP?* STOC 2008.
Arun Ramachandramurthy: Fast implementation of some SDP based approx algos: O(\sqrt{log n}) approximation
to SPARSEST CUT in O(n2) time. Sanjeev Arora, Elad Hazan, and Satyen Kale. Proc. IEEE Foundations of Computer Science, 2004.
Week 14, Wed Xi Wan: Euclidean distortion and the Sparsest Cut (S. Arora, J. R. Lee and A. Naor) Journal of the American Mathematical Society, 21(1): 1-21, 2008. [ STOC 2005 ]
Week 15, Mon Dec 07 Lei Xu: "Near-Optimal Algorithms for Maximum Constraint Satisfaction Problems," Moses Charikar, Konstantin Makarychev, Yury Makarychev, SODA 2007
Branislav Stojkovic: Luca Trevisan Approximation Algorithms for Unique Games Proc. of the 46th IEEE FOCS, 2005
Week 15, Wed Dec 09 Steve Uutarmo: Unique Games on Expanding Constraints Graphs are Easy Sanjeev Arora, Subhash Khot, Alexandra Kolla, David Steuer, Madhur Tulsiani, and Nisheeth Vishnoi. Proc. ACM STOC 2008.
Swapnoneel Roy: How to Round Any CSP - Prasad Raghavendra, David Steurer FOCS 2009


The workload will be pretty light. Other than attending the lectures, students will have to do the following:


A grade of satisfactory/unsatisfactory will be assigned at the end of the course. If you want a letter grade, talk to the instructors about more details.

Academic Honesty

We have zero tolerance for cheating and will follow the CSE Department Policies on Academic Integrity.

List of papers on LP-based approximation algorithms that students can choose to present

List of papers on SDP-based approximation algorithms that students can choose to present

(*) Algorithms to solve UGC

(*) Algorithms for approximating CSPs (*) More SDP centric algorithms. Both of the paper below use the well known multiplicative weights method from online learning to get cool results for SDPs (*) ARV related papers.