Computer Science 282

Design and Analysis of Efficient Algorithms

Fall 2012

Instructor: Daniel Stefankovic
Class: Tuesday, Thursday 11:05am-12:20pm, CSB 209.
Instructor office hours (CSB 620): Tuesday 12:30pm-1:30pm, Thursday 12:30pm-1:30pm
TAs: Tivadar Papai, Ian Perera, Julian Lunger
TA office hours: Tivadar Papai (CSB 725) Wednesday 4pm-5pm, Ian Perera (CSB 607) Monday 3pm-4pm.

Textbooks (all on a 2 hour reserve in the library):

• required: [DPV] = Algorithms, S. Dasgupta, C. Papadimitriou, U. Vazirani (a draft is available online), 2006.
  
• recommended: [CLRS] = Introduction to Algorithms (3rd edition), T. Cormen, C. Leiserson, R. Rivest, and C. Stein, 2009.

Other resources/recommended reading (all on a 2 hour reserve in the library):

• Algorithm Design, J. Kleinberg and E. Tardos, 2005.
• The Design and Analysis of Algorithms, D. Kozen, 1991.
• The Design and Analysis of Computer Algorithms, A. Aho, J. Hopcroft, J. Ulman, 1974.
• Algorithms Algorithms, R. Johnsonbaugh, M. Schaefer, 2003.
• How to Think About Algorithms Algorithms, J. Edmonds, 2008.
• Probability and Computing: Randomized Algorithms and Probabilistic Analysis, M. Mitzenmacher, E. Upfal, 2005.
• Randomized Algorithms, R. Motwani, P. Raghavan, 1995.
• Approximation Algorithms, V. Vazirani, 2004.

Prerequisites: CSC162 or CSC172 or MTH172.

Schedule

Aug. 30 Th - Introduction

TOPIC: Greedy algorithms/Dynamic programming

reading: [DPV] Section 5.2, Chapter 6, handout/homework 1

Sep. 4 Tu - When does greedy algorithm for the coin change problem work?
Sep. 6 Th - Dynamic programming for the coin change problem. Knapsack (integer weights).
Sep. 11 Tu - Knapsack revisited (integer values). Longest increasing subsequence.
Sep. 13 Th - Edit distance. Chain matrix multiplication.
Sep. 18 Tu - More dynamic programming problems.
Sep. 20 Th - EXAM #1


TOPIC: Graph algorithms

reading: [DPV] Chapters 3, 4, 5, handout/homework 2 handout/homework 2b

Sep. 25 Tu - Finding connected components, DFS, testing whether graph is strongly connected.
Sep. 27 Th - Linearization (topological sorting). Strongly connected components.
Oct. 2 Tu - BFS, Shortest paths (Dijkstra)
Oct. 4 Th - Dealing with negative edge weights(Bellman Ford). Floyd-Warshal.
Oct. 9 Tu - no class (fall break)
Oct. 11 Th - Matchings.
Oct. 16 Tu - Minimum spanning trees.
Oct. 18 Th - Flows I.
Oct. 23 Tu - Flows II.
Oct. 25 Th - EXAM #2


TOPIC: Linear programming

reading: [DPV] Chapter 7, handout/homework 3

Oct. 30 Tu - Modeling with linear programs I (classical problems).
Nov. 1 Th - Solving systems of equations (Gaussian elimination), solving systems on inequalities (Fourier-Motzkin elimination)
Nov. 6 Tu - Duality, Modeling with linear programs II (zero-sum games).
Nov. 8 Th - Linear programming for approximation (relaxation, rounding).
Nov. 13 Tu - EXAM #3


TOPIC: String matching

reading: [DPV] Chapter 2, handout/homework 4

Nov. 15 Th - Suffix trees I.
Nov. 20 Tu - Suffix trees II.
Nov. 22 Th - no class (thanksgiving)
Nov. 27 Tu - Convolution, string matching with don't cares.
Nov. 29 Th - Fast Fourier Transform
Dec. 4 Tu - EXAM #4


TOPIC: NP

reading: [DPV] Chapter 8,

Dec. 6 Th - NP completness, reductions I.
Dec. 11 Tu - NP completness, reductions II.


Comprehensive final exam

Dec. 20 Thursday FINAL EXAM (4:00pm, CSB 209) (following university final exam schedule)

Grading

• The grade for the course is the minimum of the exam grade and the homework grade.
• The in-class exams contribute 60% to the exam grade; the final exam contributes 40% to the exam grade.

Homework Rules

• Homework is collected on the due date, before class.
• No late homework will be accepted without instructor's permission (a permission must be requested at least 24 hours before the due date).
• In the final evaluation the lowest homework score will be dropped.
• You may work with other people on the homework, but you must each write up your solutions separately (without any written aid). If you work with other people, indicate who you worked with on your solution.

Test Rules

• All tests are closed book. No text or notes, no scratch paper allowed.
• There will be 4 full-class exams and a final exam. There will be no make-up exams.
• In the final evaluation everybody's one lowest exam score will be dropped.

This course follows The University Policy on Academic Honesty .