CS 7520 Approximation Algorithms

Topics

Date(s)

Reading

Introduction to approximability, approximation factors, PTAS, FPTAS,
hardness of approximation.
Vertex Cover, Metric Steiner Tree and TSP, Knapsack.

Tue, Jan 8

Reading:
Vazirani Chapters 1,3 & 8.

MAX-CNF, #DNF

Thu, Jan 10

Reading:
Vazirani Chapters 16(intro), 16.1 & 16.2
and 28 (intro) & 28.1.

Bin Packing

Tue, Jan 15

Reading:
Vazirani Chapter 9.

Makespan
Discussion on Possible Extensions of Bin Packing and Knapsack

Thu, Jan 17

Reading:
Vazirani Chapters 8 and 9.

Guest lecture from Algorithmic Game theory: Weighted Majority Theorem

Tue, Jan 22

Reading:
Adam kalai's home page, notes from CS8803

Set Cover: Basics

Thu, Jan 24

Reading:
Vazirani Chapter 2.1.

Set Cover and Set Coverage in Generality
(including costs on sets, and requirements > 1)

Thu, Jan 26

Reading:
A tighter analysis and a randomized alg.(I)
Analysis for set coverage (II)

Multiway Cut and k-Cut
Layering and General Vertex Cover

Thu, Jan 26

Reading:
Vazirani, Chapter 4, and paragraph 2.2

LP's as lower bounds
Randomized Rounding for General Vertex Cover
Primal-Dual Method, General Vertex Cover

Super Tue, Feb 5

Reading:
Vazirani, Chapters 12 and 15.

Primal-Dual Method, Steiner Forest

Thu, Feb 7

Reading:
Vazirani, Chapter 22.

Primal-Dual Method, Facility Location
(primal, dual , phase 1 of the algorithm)

Tue, Feb 12

Reading:
Vazirani, Chapter 15, in particular paragraph 15.1
Vazirani, Chapter 24,
pp 231-234.

Primal-Dual Method
Facility Location, factor 3
(primal, dual , full algorithm and analysis)

Thu, Feb 14

Reading:
Vazirani, Chapter 24,
pp 231-241.
including reading (but not ncessarily solving) the problems in pp 238-241.

Dual Fitting Method
Facility Location, factor 3
(simpler algorithm)

Tue, Feb 19

Reading:
Vazirani, Chapter 13
And these lecture notes:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Class Cancelled

Thu, Feb 21

Reading: ---

Dual Fitting Method
Facility Location, factor better than 3
via Factor Revealing LP

Tue, Feb 26

Reading:
Notes from Feb 19
and outline of original JMMSV paper.

Lagrangian Relaxation
exemplified by k-Median

Thu, Feb 28

Reading:
Vazirani, Chapter 25
paragraphs 25.1 and 25.2

Lagrangian Relaxation
exemplified by k-Median

Tue, March 4

Reading:
Vazirani, Chapter 25
finished entire chapter

MAXSAT, 3/4 Approximation
exemplifies randomization/derandomization
and smart LP rounding

Thu, March 6

Reading:
Vazirani, Chapter 16

Metric Methods, Distances as Relaxations, Metrics and Cuts
Multiway Cut and LP Rounding

Tue, March 11

Reading:
Lecture Notes.

Multiway Cut, 1.5 Approx Factor

Thu, March 13

Reading:
Vazirani, Chapter 19, paragraphs 19.1 and 19.2

Spring Break

March 19 and 21

Reading:
Have Fun !

Midterm Exam
Take Home

March 25 and 27

Reading:
Midterm.

Duality Methods in Applications (I)
Adwords and Other Auctions
Budget Allocations via Iterated Rounding

Tue, April 1

Reading:
Adwords Paper, JACM.
Budget Allocations Paper.

Duality methods in Applications (II)
Primal-Dual Schema in Parallel

Thu, April 3

Reading:
Parallel Set Cover Paper.

Approximate Counting (Ia)
Counting Matchings via Sampling
Sampling via Rapid Mixing Markov Chains
Rapid Mixing via Conductance

Tue, April 8

Reading:
Jerrum and Sinclair's Survey.

Approximate Counting (Ib)
Conductance by Bounding Congestion using Canonical Paths

Thu, April 10

Reading:
Jerrum and Sinclair's Survey.

Approximate Counting (II)
Network reliability, emphasis on enumerating small cuts

Tue, April 15

Reading:
Vazirani, Chapter 28
emphasis on 28.2.1

Strict Quadratic Programs and Vector Program Relaxations
(Positive Semidefinite Programs as a black box to solve Vector Programs)
0.87856 Approx for MAXCUT and MAX2SAT

Thu, April 17

Reading:
Vazirani, Chapter 26
emphasis on 26.1, 26.4, 26.5

Sparsest Cut O(logn) Approximation (I)

Tue, April 22

Reading:
Vazirani, Chapter 21

Sparsest Cut O(logn) Approximation (II)

Tue, April 22

Reading:
Vazirani, Chapter 21