CS 312, Sections 001 & 002
Algorithm Analysis
Winter 2008

Date

Lecture

Topics

Reading
(Read before class)

Projects
(dates of availability)

Deadlines
(Homework due in class at start of class;
Project and improvement reports due by 5pm)

Week 1

1/7

1

Course objectives;
What is an algorithm?;
Algorithm efficiency;
The Three Questions; Asymptotic notation

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1/9

2

Asymptotic notation: Duality, Limit rule;
First Foray in Analysis: Algorithms for Arithmetic

Chapter 0; Sections 1.1 and 1.2

(Light) Project #1: Simple Fermat Primality Tester (for small integers)

Install Visual Studio (see directions in the course Syllabus)

1/10

-

Help Session: Project #1
Also: Intro. to Visual Studio & C#
[3pm in 1066 TMCB]

Project #1 Guidelines;
Intro. to C# on MSDN

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1/11

3

Asymptotic notation: Max rule;
Modular arithmetic, including Modular exponentiation

Section 1.3

HW #1: 0.1 (a-e, g, m), 0.3 (a,b) in the textbook

Week 2

1/14

4

Primality testing; Greatest Common Divisor

Section 1.4

HW #2: 1.25 in the textbook, then redo 1.25 using 126 for the exponent

1/16

5

Public Key Cryptography: RSA

Section 1.4

HW #3: 1.9, 1.18, 1.20 in the textbook

1/18

6

Divide & Conquer Multiplication;
Master Theorem;
Examples: Convex Hull, Binary Search

Sections 2.1 and 2.2

Project #2: Divide & Conquer - Convex Hull

Week 3

1/21

Holiday: Martin Luther King, Jr. Day

1/22

-

Help Session: Project #2
[3pm in 1066 TMCB]

Project #2 Guidelines

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1/23

7

Intro. to Recurrence Relations;
Solving homogeneous RRs

Recurrence Relations Notes, Part I

HW #4: 1.27, 2.1, 2.5(a-e) in the textbook; for 2.5 (a-e), only find bounds using the Master Theorem

1/25

8

Non-homogeneous recurrence relations (with geometric forcing function)

Recurrence Relations Notes, Part II

1/25

-

Help Session: Project #2
[3pm in 1066 TMCB]

Project #2 Guidelines

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Week 4

1/28

9

Recurrence relations: change of variable

Recurrence Relations Notes, Parts III & IV

1/30

10

Theoretical and empirical analysis of mergesort and quicksort

Section 2.3

2/1

11

Sections 2.4 and 2.5

HW #7: Part III (Section 3.2) Exercises 1 and 2 in the RR Notes;
+ Analyze 3-part Mergesort using Recurrence Relations solution techniques;
+ 2.4 in the text book (using the Master Theorem where possible)

Week 5

2/4

12

Fast Fourier Transform (FFT)

Section 2.6

Project #3: Graph Algorithms - Separating Vertices, Bridges, and Biconnected Components

Improvement #2

2/5

-

Help Session: Project #3
[3pm in 1066 TMCB]

Project #3 Guidelines

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2/6

13

Graph algorithms: Formulating problems as graphs;
Depth-first Search and Connected Components

Chapter 3.1-3.2

2/8

14

Directed Graphs, Linearization, Connectedness

Section 3.3

Week 6

2/11

15

Strongly connected components

Section 3.4

HW #9: 3.31in the textbook; this is critical for Proj. #3

2/12

-

Help Session: Project #3
[3pm in 1066 TMCB]

Project #3 Guidelines

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2/13

16

Breadth-first search; Shortest Paths;
Dijkstra's algorithm

Sections 4.1-4.5

HW #10: 3.4 (graph ii only), 3.10, 3.15 in the textbook

2/15

17

Dijkstra's algorithm; Efficiency with various Priority Queue implementations;
Special cases for Shortest Paths;
Bellman-Ford algorithm

Sections 4.6-4.7

HW #11: 4.1in the textbook

Week 7

2/18

Holiday: President's Day

2/19
Monday Instruction

18

Greedy algorithms:
Coins;
Minimal spanning trees,
Kruskal's algorithm

Section 5.1

Project #3

2/20

19

Representing disjoint sets;
Analysis of Kruskal's;
Prim's algorithm for MST

Section 5.1

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2/22

20

(Divisible) Knapsack;
Huffman Encoding

Section 5.2; (Sections 5.3-5.4)

Project #4: Intelligent Scissors

Improvement #3

Week 8

2/25

21

Dynamic Programming;
Binomial Coefficients;
Coins;
Extracting solutions

Sections 6.1-6.2

HW #12: described in separate document

2/26

-

Help Session: Project #4
[3pm in 1066 TMCB]

Project #4 Guidelines

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2/27

-

Review: Mid-Term Exam

Study List of Topics for Mid-Term Exam

2/28

Mid-Term Exam in Testing Center

2/29

3/1

Week 9

3/3

22

Optimality in DP;
Edit Distance;
Gene Sequence Alignment

Section 6.3

HW #13: described in separate document

3/5

23

0/1-Knapsack

Section 6.4

Project #4

3/7

-

Follow-up: Mid-Term Exam

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Week 10

3/10

24

Chain Matrix Multiplication;
Extra: Recursion and Memory functions (Memoization)

Section 6.5

Project #5: Gene Sequence Alignment

3/11

-

Help Session: Project #5
[3pm in 1066 TMCB]

Project #5 Guidelines

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3/12

25

All-Pairs Shortest Paths; Floyd's Algorithm

Section 6.6; (Section 6.7)

HW #15: described in separate document

3/14
Happy p Day!

26

Linear Programming; Standard Form

Section 7.1

HW #16: described in separate document

3/15

-

College of Physical and Mathematical Sciences
Spring Research Conference
[8am in 1104 JKB]

Week 11

3/17

27

Flows in Networks

Section 7.2

3/19

28

Flows in Networks (cont.); Examples; Bipartite Graphite Matching

Sections 7.3-7.4

3/21

29

Simplex Algorithm

Section 7.6;
Linear Programming Notes (Important for the Project)

Week 12

3/24

30

Review: Tractability, P, NP, and NP-Complete

Section 8.2: pp. 243-247 

(Light) Project #6: Linear Programming

3/25

-

Help Session: Project #6
[3pm in 1066 TMCB]

Project #6 Guidelines

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3/26

31

Back-tracking search: Graph coloring, 8 Queens;
Feasibility functions

Keep working on Project #6 -- finish early!

3/28

32

Guided search;
Bound functions;
Branch and Bound search for Job Assignment

HW #19: described in separate document

Week 13

3/31

33

Solving the TSP with Branch and Bound

Branch &Bound for TSP Notes
(Useful for the Project)

4/2

34

4/3

-

(Rescheduled) Help Session: Project #7
[3pm in 1066 TMCB]

Project #7 Guidelines

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4/4

35

Best-first Search;
A* Search and Admissible Heuristics
and relation to Branch & Bound

HW #21: described in separate document

Week 14

4/7

36

Randomized Algorithms;
Monte Carlo Algorithms;
Amplification of Stochastic Advantage

"Virtual Chapter" (beginning with the gray box on p. 29)

4/9

37

Amplification of Stochastic Advantage (cont.)

4/11

38

Numerical Probabilistic Algorithms;
Las Vegas Algorithms

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HW #22: described in separate document

Week 15

4/14

-

Last day of CS 312
Review: Final Exam

Study List of Topics for Final Exam

Project #7
(No Improvement #7)

4/15

-

Last day of Winter Instruction  (no CS 312)

4/16

-

Reading days

4/17

4/18
Friday

-

Final Exam for Section 002: 11:00am-2:00pm in Classroom

4/19
Saturday

-

Final Exam for Section 001: 2:30pm-5:30pm in Classroom