Instructor
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Instructor
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Class MeetingsTBA |
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.) |
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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. |
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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) |
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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. |
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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. |
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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. |
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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 |
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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 |
(*) Algorithms to solve UGC