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Announcements


• 05/18.Check out the following survey reports: (wisc.edu access only)
  Online optimization algorithms [PDF] by Dave Andrzejewski
  Bounds on alphabet size and rate for network coding [PDF] by Siddharth Barman
  Network coding [PDF] by Matt Elder
  Stochastic optimization [PDF] by Chi Man Liu
• 05/10. The final exam [PDF] is available now. It is due by midinght on May 15.
• 05/10. You can now download all the scribe notes in a single PDF. See below.

Course Description

The field of approximation algorithms has developed in response to the difficulty in solving a good many optimization problems exactly. This course will present general techniques that underly these algorithms. Read more ...


Scribe notes & readings

Here are all the scribe notes in one file: [PDF]


1. (1/23) Intro, vertex cover, TSP. [PDF]
2. (1/25) Steiner tree, Greedy approximations: multiway cut. [PDF]
3. (1/30) Greedy approximations: set cover, makespan. [PDF]
4. (2/1)   Edge disjoint paths, DP-based algorithms: FPTAS for knapsack. [PDF]
             Chekuri and Khanna's paper on EDP
5. (2/6)   Bin-packing, Euclidean TSP. [PDF]
6. (2/8)   Euclidean TSP (contd.) [unedited PDF]
             Lecture notes by Michel Goemans
7. (2/13) Local search: max-cut, facility location [PDF]
             Korupolu et al.'s paper for facility location. Arya et al.'s improved analysis.
             Survey by David Shmoys on algorithms for k-median and facility location.
8. (2/15) Facility location (contd.), min degree spanning tree [PDF]
             Furer and Raghavachari's paper on min degree spanning trees.
9. (2/20) Linear Programming [PDF]
10. (2/22) LP rounding: vertex cover, facility location (see lect 9 & 11 for notes)
11. (2/27) Facility location (contd.), Randomized rounding: set cover, routing [PDF]
              Shmoys, Tardos and Aardal's paper on LP-rounding for facility location.
              Lecture notes on Chernoff bounds and min-congestion routing.
12. (2/29) min-congestion routing (contd.), LP duality and the primal-dual method [PDF]
              Raghavan and Thompson's paper introducing randomized rounding.
              Survey by David Williamson on the primal-dual method.
13. (3/6)   Primal-dual: Vertex cover, Steiner forest [PDF]
14. (3/8)   Primal-dual: Steiner forest (contd.), facility location [PDF]
15. (3/13) Facility location (contd.); Cut LPs and metrics [PDF]
16. (3/15) Multiway cut, Multicut via region growing [PDF]
              Survey by David Shmoys on multicut, sparsest cut, and their applications.
              The original multicut paper by Garg, Vazirani and Yannakakis.
17. (3/20) Sparsest Cut, Balanced cut: O(log k log D)-approx [PDF]
18. (3/21) Balanced Cut (contd.), Sparsest Cut & embeddings into ell_1 [PDF]
              For more applications of sparsest cut and balanced cut, see the survey by David Shmoys
19. (3/22) Bourgain's embedding into ell_1, Semi-Definite Programming [PDF]
              This paper by Linial, London & Rabinovich has a number of nice theorems about embeddings apart from the approximation to sparsest cut.
20. (3/27) SDP: Max-cut, max-2-SAT [PDF]
              A really good survey by Helmberg on the techniques for solving SDP and its applications to NP-hard optimization problems.
              For more on the theory of SDP and SDP duality, see this survey by Vandenberghe and Boyd.
              Goemans and Williamson's max-cut paper.
21. (3/29) SDP: Coloring [PDF]
              Karger, Motwani & Sudan's paper, and Blum & Karger's improvement.
22. (3/30) Approximation via tree embeddings [PDF]
23. (4/10) Low diameter partitioning, and approximating metrics by tree metrics [PDF]
              Bartal's second paper on embeddings into trees, and the FRT optimal result.
24. (4/12) Approximate counting, sampling [PDF]
              A very nice set of lecture notes by Mark Jerrum.
25. (4/24) Markov Chain Monte Carlo, random walks and mixing [PDF]
              Survey on rapid mixing by Jerrum and Sinclair including conductance and the canonical paths argument. Chapter on coupling by Jerrum.
26. (4/26) MCMC contd. and Lagrangean techniques [PDF1 and PDF2]
27. (4/27) Inapproximability [PDF]
28. (5/1)   PCPs and hardness of approximating Max3SAT [PDF]
29. (5/3)   Hardness of approximating set cover [PDF]


Homeworks
(Solutions are not available any more. Sorry!)


1. HW1 [PDF] [Solutions]
2. HW2 [PDF] [Solutions]
3. HW3 [PDF] [Solutions]


Misc material

Project ideas are available here.
A template for scribe notes can be found here.
Before scribing lectures, please read this note on mathematical writing by Knuth, Larrabee and Roberts.