We will not follow any specific textbook. However, Vijay Vazirani's book Approximation Algorithms is a great introduction to the area and contains many of the topics we will cover.
There will be 4-5 homework assignments.
Detailed description of topics covered
Jan. 6: Definition of approximation algorithms; factor-2 approximation for Job Interval Scheduling; greedy algorithm for unweighted Set Cover; notion of hardness of approximation.
Jan. 8: Greedy algorithm for weighted Set Cover; application to Shortest Superstring; defined minimum Steiner Tree problem.
Jan. 13: Approximation preserving reductions; 2-approximation for Steiner Tree, 1.5-approximation for Metric Traveling Salesman and O(log n)-approximation for Asymmetric Traveling Salesman.
Jan. 15: Local Ratio. Approximation algorithms for Vertex Cover, Steiner Forest and Job Interval Selection problems.
Jan. 20: 2-approximation for symmetric k-center and 3-approximation for the weighted version.
Jan. 22: An O(log*n)-approximation algorithm for asymmetric k-center.
Jan. 27: Hardness of approximation for asymmetric k-center.
Jan. 29: PTAS for knapsack and bin packing.
Feb. 3: PTAS for Euclidean TSP.
Feb. 5: Linear programming, randomized rounding and integrality gaps. LP-rounding algorithms and integrality gaps for Vertex Cover, Set Cover, Machine Scheduling.
Feb. 12: Congestion Minimization, Edge Disjoint Paths, hardness of directed EDP.
Feb. 17: Multiway Cut, a factor (2-1/k)-approximation algorithm.
Feb. 19: Primal-Dual method, complementary slackness conditions. Primal-dual algorithm for Set Cover. Min-Cut Max-Flow theorem via LP-duality and LP-rounding.
Feb. 24: A 2-approximation for multicut on trees via the primal-dual method. Solving the multicut LP relaxation using Ellipsoids algorithm with a separation oracle.
Feb. 26: Approximation algorithm for directed multicut; O(log k)-approximation for undirected multicut and matching lower bound on flow-cut gap.
Mar. 3: Sparsest cut: definitions, LP relaxation, approximation via minimum multicut.
Mar 5: Sparsest cut: logarithmic approximation via Bourgain's theorem.
Mar. 10: Will finish proof of Bourgain's theorem. Semidefinite programming, SDP-rounding for Max Cut.