15-750 Graduate Algorithms (Spring 2005) (original) (raw)

No.

Date

Topics

Readings

Homework

1

01/10 M

Introduction, Algorithm, Complexity, Various Equalities, Graphs, Recursion Tree, Master Theorem, Akra-Bazzi Theorem, Divide and Conquer (Strassen, Binary Multiplication), Dynamic Programming, Breadth First Search, Topological Sort, Minimum Spanning Trees, Shortest Paths

[Kozen 1] [CLR 1, 2, 3, 4, 5.4]

Homework 0 (PS) Solution (PS)

2

01/12 W

Hints, Depth First Search, Strongly Connected Components

[Kozen 2, 4, 5] [CLR 23, 24, 25]

3

01/14 F

More strongly connected components, minimum spanning forest

[Kozen 4] [CLR 23, 24]

4

01/17 M

(Martin Luther King Day) NO CLASS

5

01/19 W

Union-Find, Analysis

[Kozen 10,11] [CLR 22]

Homework 0 Due. Homework 1 (PS) Solution (PS)

6

01/21 F

Heaps, Binomial Heaps, Amortized Analysis of Binomial Heaps

[Kozen 8] [CLR 20]

7

01/24 M

Fibonacci Heaps

[Kozen 9] [CLR 21]

8

01/26 W

More Fibonacci Heaps

[Kozen 9] [CLR 21]

9

01/28 F

Treaps (Random Search Trees)

[Kozen 13] [M&R 8.2]

Homework 1 Due. Homework 2 (PS) Q1 picture Solution

10

01/31 M

More Treaps

[Kozen 13]

11

02/02 W

Splay Trees

[Kozen 12] Sleator's note

12

02/04 F

Splay Trees Proof

[Kozen 12]

Practice Midterm Solution

13

02/07 M

No class

14

02/09 W

Midterm 1 -- Part 1

15

02/11 F

Midterm 1 -- Part 2

16

02/14 M

Planar Graphs, 5-coloring

17

02/16 W

Planarity Testing

[Kozen 14]

18

02/18 F

Planar Separator Theorem 1

[Kozen 15]

19

02/21 M

Subhash Khot's Talk (Attendence not required)

20

02/23 W

Planar Separator Theorem 2

[Kozen 15]

Homework 3 (PS) Solution

21

02/25 F

Planar Separators

[Kozen 15]

22

02/28 M

NP-Completeness 1 (Introduction)

[Kozen 21, 22, 23, 24] [CLR 36]

23

03/02 W

NP-Completeness 2 (Random NP Problems)

[Kozen 21, 22, 23, 24] [CLR 36]

24

03/04 F

Mid-Semester Break; No Class

03/07 M

----------------- (Spring Break)

03/09 W

----------------- (Spring Break)

03/11 F

----------------- (Spring Break)

25

03/14 M

NP-Completeness 3 (NP, co-NP, NP-hard, Independent Set)

[Kozen 21, 22, 23, 24] [CLR 36]

26

03/16 W

NP-Completeness 4 (Independent Set and Cook's Theorem)

[Kozen 21, 22, 23, 24] [CLR 36]

27

03/18 F

NP-Completeness 5 (Cook's Theorem)

[Kozen 21, 22, 23, 24] [CLR 36]

28

03/21 M

NP-Completeness 6 (Hamiltonian Cycle to SAT)

[Kozen 21, 22, 23, 24] [CLR 36]

29

03/23 W

Guest Lecturer: Anupam Gupta on Approximation Algorithms

[CLR 37]

Homework 4 (PS) Solution (PS)

30

03/25 F

Randomized 2-SAT

31

03/28 M

Polynomial identity checking

[Kozen 40] [M&R 7.2]

32

03/30 W

Polynomial identity checking

[Kozen 40] [M&R 7.2]

33

04/01 F

Midterm 2

34

04/04 M

Matching

[Kozen 19, 20] [M&R 7.3]

35

04/06 W

RP, Randomized Algorithms -- Test of Associativity

36

04/08 F

RP, Randomized Algorithms

37

04/11 M

Random Walks -- 1, 2, and 3 dimensions

[M&R 6]

38

04/13 W

String and Set Equality

39

04/15 F

No class (Spring Carnival)

Homework 5 (PS) Solution

40

04/18 M

Random Walks on General Graph

[M&R 6]

41

04/20 W

How to Write a Proof

42

04/22 F

The probabilistic method - Max-Cut; Randomized and Deterministic 1/2-Approximation Algorithms for Max-Cut

[M&R 5.1]

43

04/25 M

Final Review by Chris and Virginia

45

04/27 W

Free Cake: Cake Cutting

44

04/29 F

"Sunny" Day, No Class

46

05/05 Thursday

Final Exam. 8:30a.m. to 11:30a.m. DH 2302