6.854J | Fall 2005 | Graduate
Advanced Algorithms


1 Course Introduction
Fibonacci Heaps

Persistent Data Structures

3 Splay Trees

4 Splay Trees (cont.)
Suffix Trees
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.)

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

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
Course Info
As Taught In
Fall 2005
Learning Resource Types
assignment_turned_in Problem Sets with Solutions