51815 | Fall 2018 | M W 2-3:30 | RLP 0.104
Instructor: Dana Moshkovitz
This class is about approximation algorithms and their limitations. It covers: combinatorial approximation algorithms; approximation algorithms based on linear programming (LP) and semidefinite programming (SDP); hierarchies of linear and semidefinite programming; limitations on LP and SDP; hardness of approximation and connections to multi-prover games and probabilistic checking of proofs; the proof of the PCP theorem, including combinatorial and algebraic techniques; sum-check; linearity testing; low degree testing; locally testable and decodable codes; composition; parallel repetition; long code, Fourier analysis and optimal inapproximability results; the Unique Games Conjecture; dictator tests and integrality gaps.
Format: Some of the meetings will be regular lectures, and some will be “workshops” in which the students give mini-lectures. Before each workshop there will be a schedule with the topics of the mini-lectures. Usually there will be problems to solve and a mini-lecture will present a solution, but sometimes mini-lectures will be surveys or discussions of open problems. Students should register to give mini-lectures after the release of each workshop schedule. Workshops will give students ample opportunity to give lectures and receive feedback. There are no exams or problem sets apart from workshop participation and presentation.
|
|
Date |
Topic |
|
1 |
Wednesday, August
29 |
Overview; basic combinatorial approximation algorithms:
vertex cover, set cover, 3SAT |
|
|
Monday, September
3 |
Labor Day |
|
2 |
Wednesday,
September 5 |
|
|
3 |
Monday,
September 10 |
Workshop on approximation
basics, including constraint satisfaction problems, label-cover, unique
label-cover |
|
4 |
Wednesday,
September 12 |
The
primal-dual method |
|
5 |
Monday,
September 17 |
Workshop
on approximation algorithms based on linear programming |
|
6 |
Wednesday, September
19, |
Semidefinite programming (SDP), Max-Cut
approximation and integrality gap |
|
7 |
Monday, September
24, |
|
|
8 |
Wednesday, September
26, |
|
|
9 |
Monday, October
1 |
|
|
10 |
Wednesday, October
3 |
Hardness of Approximation, Multi-prover games and
probabilistic checking of proofs (PCP) |
|
11 |
Monday,
October 8 |
|
|
12 |
Wednesday,
October 10 |
|
|
13 |
Monday,
October 15 |
|
|
14 |
Wednesday,
October 17 |
Fourier
analysis |
|
15 |
Monday,
October 22 |
Workshop on Fourier
analysis |
|
16 |
Wednesday,
October 24 |
Hadamard-based
PCP |
|
17 |
Monday,
October 29 |
Workshop on Hadamard-based PCP |
|
18 |
Wednesday,
October 21 |
Sum-Check
and PCP with polylog queries |
|
19 |
Monday,
November 5 |
Workshop on sum-check and its
many applications, low degree testing |
|
20 |
Wednesday,
November 7 |
Composition,
PCP of proximity, robust PCP, decoding PCP |
|
21 |
Monday,
November 12 |
Workshop on composition,
connection to code concate |
|
22 |
Wednesday,
November 14 |
Gap
amplification (powering) |
|
23 |
Monday,
November 19 |
Parallel repetition |
|
Wednesday,
November 21 |
Thanksgiving |
|
|
24 |
Monday,
November 26 |
Workshop on gap
amplification and parallel repetition |
|
25 |
Wednesday,
November 28 |
The
long code and optimal inapproximability |
|
26 |
Monday,
December 3 |
Workshop on long code and
optimal inapprox |
|
27 |
Wednesday,
December 5 |
The
Unique Games Conjecture |
|
28 |
Monday,
December 10 |
Workshop on the Unique
Games Conjecture |