Advanced Algorithms

Calendar

LEC #	TOPICS	KEY DATES
1	Course Introduction Fibonacci Heaps
2	MST Persistent Data Structures
3	Splay Trees
4	Splay Trees (cont.) Suffix Trees Tries	Problem set 1 due
5	Suffix Trees (cont.) Tries (cont.) Dial’s Algorithm
6	Dijkstra’s Algorithm Van Emde Boas Queues	Problem set 2 due
7	Van Emde Boas Queues (cont.) Hashing
8	2-Level Hashing Network Flows
9	Network Flows: Augmenting Paths, Maximum Augmenting Paths, Scaling	Problem set 3 due
10	Reductions between Flow Problems Bipartite Matching Shortest Augmenting Path Blocking Flows
11	Blocking Flows (cont.)
	Recitation Topics: Dynamic Trees, Push-Relabel Max-Flow Algorithm
12	Min-Cost Flows	Problem set 4 due
13	Min-Cost Flows (cont.) Linear Programming	Problem set 5 due
14	Linear Programming (cont.) Structure of Optima Weak Duality
15	Linear Programming (cont.) Strong Duality
	Recitation Topic: Simplex	Problem set 6 due
16	Linear Programming (cont.) Complementary Slackness Algorithms: Simplex, Ellipsoid
17	Linear Programming (cont.) Algorithms: Interior Point NP-hard problems	Problem set 7 due two days after Lec #17
18	Approximation Algorithms
19	4/3-Approximation for TSP
20	Relaxations Directed TSP	Problem set 8 due
21	Randomized Rounding Chernoff Bound Fixed Parameter Tractability Kernelization
22	Online Algorithms (Ski Rental, Load Balancing, Paging)	Problem set 9 due
23	Randomized Online Algorithms (Adversaries, Fiat’s Marking Algorithm, Potential Functions, Yao’s Minimax Principle)
24	K-Server Problem Double-Coverage Algorithm Computational Geometry Introduction (Orthogonal Range Search)	Problem set 10 due
25	Sweep Algorithms (Convex Hull, Segment Intersection, Voronoi Diagrams)
26	Sweep Algorithms (Voronoi Diagrams) Randomized Incremental Constructions Backwards Analysis Linear Programming in Fixed Dimension	Problem set 11 due two days after Lec #26
27	(Optional Material) External Memory Algorithms	Problem set 12, problem 1 due
28	(Optional Material) Cache Oblivious Algorithms: Matrix Multiplication, Linked Lists, Median
29	(Optional Material) Cache Oblivious Algorithms: Search Streaming Model	Rest of problem set 12 due three days after Lec #29