CS 312, Sections 001 & 002
Algorithm Analysis
Winter 2009

Date

Lecture

Topics

Reading
(Read before class)

Assignment Due Dates
(Homework due in class at start of class;
Project reports due by 5pm submitted online.)

Week 1

1/5

1

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

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1/7

2

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

Course Syllabus and Schedule;
Chapter 0; Sections 1.1 and 1.2

Install Visual Studio (see directions in the course Syllabus)

1/8

-

Help Session: Project #1
Also: Intro. to Visual Studio & C#
[4pm in 1060 TMCB]

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

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1/9

3

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

Section 1.3

HW #1: 0.1 (a-e, g, m), 0.3 (a) in the textbook;
New: 0.3 (b) is extra credit

Week 2

1/12

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

1/14

5

Public Key Cryptography: RSA

Section 1.4

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

1/16

6

Divide & Conquer Multiplication;
Master Theorem;
Example: Convex Hull

Sections 2.1 and 2.2

Week 3

1/19

Holiday: Martin Luther King, Jr. Day

1/20

-

Help Session: Project #2
[4pm in 1029 TMCB]

Project #2 Guidelines

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1/21

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

1/20

-

Help Session: Project #2
[4:15pm in 1029 TMCB]

Project #2 Guidelines

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1/23

8

Non-homogeneous recurrence relations (with geometric forcing function)

Recurrence Relations Notes, Part II

Week 4

1/26

9

Recurrence relations: change of variable;
Theoretical analysis of mergesort;
Proof of Master Theorem

Recurrence Relations Notes, Parts III & IV

1/28

10

Theoretical and analysis of quicksort, worst case, best case, and average case;
Empirical analysis of both mergesort and quicksort

Section 2.3

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)

1/30

11

Sections 2.4 and 2.5

Project #2: Divide & Conquer - Convex Hull

Source Code Distribution

Week 5

2/2

12

Convolution;
Fast Fourier Transform (FFT)

Section 2.6

Project #2 on-time submission until noon
[due to power outage and electrical upgrade]

2/4

13

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

Chapter 3.1-3.2

2/5

-

Help Session: Project #3, part A
[4pm in 1029 TMCB]

Project #3 Guidelines

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2/6

14

Directed Graphs, Linearization, Connectedness

Section 3.3

Week 6

2/9

15

Strongly connected components

Section 3.4

HW #9.2: 3.31 g-h in the textbook; critical for Proj. #3;

2/10

-

Help Session: Project #3, part B
[4pm in 1029 TMCB]

Project #3 Guidelines

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2/11

16

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

Sections 4.1-4.5

HW #10: 3.4 (graph ii only; start the SCC-finding algorithm at a vertex other than A -- we already did that in class), 3.10 (this one is important for project #3 as well), 3.15 -- all in the textbook

2/13

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: 4.1 in the textbook

Week 7

2/16

Holiday: President's Day

2/17
Monday Instruction

18

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

Section 5.1

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

Source Code Distribution

2/17

-

Help Session: Project #4
[4pm in 1029 TMCB]

Project #4 Guidelines

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2/18

19

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

Section 5.1

HW #12: 4.2, 5.1 a-b in the textbook

2/20

20

(Divisible) Knapsack

Section 5.2; (Sections 5.3-5.4)

HW #13: 5.2a in the textbook

Week 8

2/23

21

Dynamic Programming;
Binomial Coefficients;
Coins;
Extracting solutions

Sections 6.1-6.2

HW #14: described in separate document

2/25

22

Optimality in DP;
Edit Distance;
Gene Sequence Alignment

Section 6.3

HW #15: described in separate document

2/27

23

0/1-Knapsack

Section 6.4

Project #4: Intelligent Scissors

Source Code Distribution

Week 9

3/2

24

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

Section 6.5

HW #16: described in separate document

3/3

-

Help Session: Project #5
[4pm in 1029 TMCB]

Project #5 Guidelines

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3/4

-

Review: Mid-Term Exam

Study List of Topics for Mid-Term Exam

3/5

Mid-Term Exam in Testing Center

3/6

3/7

Week 10

3/9

25

All-Pairs Shortest Paths; Floyd's Algorithm

Section 6.6; (Section 6.7)

HW #17: described in separate document

3/11

26

Linear Programming; Standard Form

Section 7.1

3/13

-

Follow-up: Mid-Term Exam

Project #5: Gene Sequence Alignment

Source Code Distribution

Week 11

3/16

27

Flows in Networks

Section 7.2

3/17

-

Help Session: Project #6
[4pm in 1029 TMCB]

Project #6 Guidelines

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3/18

28

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

Sections 7.3-7.4

3/20

29

Simplex Algorithm

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

3/21

-

College of Physical and Mathematical Sciences
Spring Research Conference
[8am-1pm in 1104 JKB]

Week 12

3/23

30

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

Section 8.2: pp. 243-247 

3/25

31

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

Project #6: Linear Programming

(no code distribution)

3/26

-

Help Session: Project #7
[4pm in 1029 TMCB]

Project #7 Guidelines

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3/27

32

State-space search and Bound functions;
Branch and Bound search for Job Assignment

Week 13

3/30

33

Tight bounds;
Solving the TSP with Branch and Bound

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

HW #22: described in separate document

4/1

34

4/3

35

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

HW #24: described in separate document

Week 14

4/6

36

A* (cont.);
Relaxed Problems: solutions as bounds / heuristics

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Project #7: Solving the TSP with Branch & Bound

Source Code Distribution

4/8

37

Randomized Algorithms;
Monte Carlo Algorithms;
Amplification of Stochastic Advantage

No homework due -- make progress on your improvement!

4/10

38

Amplification of Stochastic Advantage (cont.)

Bonus lecture #39: Numerical Probabilistic Algorithms and Las Vegas Algorithms

HW #25: described in separate document

Week 15

4/13

-

Last day of CS 312
Review: Final Exam

Study List of Topics for Final Exam

Early: Improvement Report

4/14

-

Last day of Winter Instruction  (no CS 312)

Improvement Report

4/15

-

Reading days

4/16

4/20
Monday

-

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

4/21
Tuesday

-

Final Exam for Section 001: 11:00am-2:00pm in Classroom