Computer Science 282/482

Design and Analysis of Efficient Algorithms

Fall 2017

Instructor: Daniel Stefankovic
Class: Tuesday, Thursday 11:05am-12:20pm, Wegmans 1400.
Instructor office hours (Wegmans 2315): Tuesday 12:30pm-1:30pm, Thursday 12:30pm-1:30pm.
TAs: Jackson Abascal, Ben King, Shir Maimon, Ben Nemeth, Andrew Read-McFarland, Eric Weiss, Conrad Wehner, Brandon Willet.
TA office hours: Andrew Read-McFarland (Wegmans 3209): Monday 4pm-5pm, Wednesday 4pm-5pm.

Problem sessions (only in weeks with exams or when homework is due):

• Monday 6:15pm - 7:15pm in Hylan 202
• Tuesday 6:15pm - 7:15pm in Goergen 109
• Wednesday 6:15pm - 7:15pm in Gavett 310
• Wednesday 7:40pm - 8:40pm in Hutchinson 473

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

• recommended (available in the campus bookstore): [CLRS] = Introduction to Algorithms (3rd edition), T. Cormen, C. Leiserson, R. Rivest, and C Stein, 2009.
  
• recommended: [DPV] = Algorithms, S. Dasgupta, C. Papadimitriou, U. Vazirani, 2006.

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

• Algorithms, J. Erickson, 2013.
• 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.
• Algorithms, R. Sedgewick, K. Wayne, 2011.
• The Algorithm Design Manual, S. Skiena, 2008.

Prerequisites: CSC162 or CSC172 or MTH172.

Schedule

TOPIC: Dynamic programming (homework #1 due Sep. 7, exam #1 on Sep. 14)

Reading:
• [CLRS] Chapter 15,
• dynamic programming (Erickson),
• [DPV] Section 5.2, Chapter 6,
• advanced dynamic programming (Erickson).

homework 1

Aug. 31 Th - Dynamic programming for the coin change problem. Knapsack (integer weights).


Sep. 5 Tu - Knapsack revisited (integer values). Longest increasing subsequence.
Sep. 7 Th - Edit distance. Chain matrix multiplication.


Sep. 12 Tu - More dynamic programming problems.
Sep. 14 Th - EXAM #1 (topics: Dynamic programming)


TOPIC: Graph algorithms (homework #2 due Oct. 5, homework #3 due Oct. 19, exam #2 on Oct. 26)

Reading:
• [CLRS] Chapters 22, 23, 24, 25, 26 (excluding sections 26.4, 26.5),
• basic graph algorithms (Erickson),
• [DPV] Chapters 3, 4, 5.

homework 2
homework 3.

Sep. 19 Tu - Finding connected components, DFS, testing whether graph is strongly connected
Sep. 21 Th - Linearization (topological sorting). Strongly connected components.


Sep. 26 Tu - BFS, Shortest paths (Dijkstra)
Sep. 28 Th - Dealing with negative edge weights (Bellman Ford). Floyd-Warshal.


Oct. 3 Tu - Matchings I.
Oct. 5 Th - Matchings II.


Oct. 10 Tu - No class (Fall break).
Oct. 12 Th - Minimum spanning trees.


Oct. 17 Tu - Flows I.
Oct. 19 Th - Flows II.


Oct. 24 Tu - More graph algorithms.
Oct. 26 Th - EXAM #2 (topics: Graph algorithms)


TOPIC: Linear programming (homework #4 due Nov. 9, exam #3 on Nov. 16)

reading:
• [CLRS] Chapter 29,
• linear programming (Erickson),
• [DPV] Chapter 7.

homework 4.


Oct. 31 Tu - Modeling with linear programs I (classical problems).
Nov. 2 Th - Solving systems of equations (Gaussian elimination), solving systems on inequalities (Fourier-Motzkin elimination)


Nov. 7 Tu - Duality, Modeling with linear programs II (zero-sum games).
Nov. 9 Th - Linear programming for approximation (relaxation, rounding).


Nov. 14 Tu - Solving linear programs.
Nov. 16 Th - EXAM #3 (topics: Linear programming)


TOPIC: Divide and Conquer Algorithms (homework #5 due Dec. 7)

reading:
• [CLRS] Chapters 4, 9,30,
• FFT (Erickson),
• [DPV] Chapter 2.

homework 5

Problem sessions:
• Dec. 4 (Monday) 6:15pm - 7:15pm in Hylan 202
• Dec. 5 (Tuesday) 6:15pm - 7:15pm in Goergen 109
• Dec. 6 (Wednesday) 6:15pm - 7:15pm in Gavett 310
• Dec. 6 (Wednesday) 7:40pm - 8:40pm in Hutchinson 473


Nov. 21 Tu - recurrences, Karatsuba-Offman algorithm
Nov. 23 Th - No class (Thanksgiving).
Nov. 28 Tu - Fast fourier transform, convolution
Nov. 30 Th - deterministic linear-time k-select algorithm
Dec. 5 Tu - randomized linear-time k-select algorithm


TOPIC: NP

reading:
• [CLRS] Chapter 34,
• NP (Erickson),
• [DPV] Chapter 8.

Dec. 7 Th - NP completness, reductions I.
Dec. 12 Tu - NP completness, reductions II.


Comprehensive final exam

Dec. 21 Thursday FINAL EXAM (4:00pm-7:00pm, Douglass Ballroom) (following university final exam schedule)

Grading

• The grade for the course is computed from the exam grade (54%), the homework grade (10%), and the final exam grade (36%).

Homework Rules

• Homework is collected on the due date, before class, in the classroom.
• No late homework will be accepted without instructor's permission (a permission must be requested at least 24 hours before the due date).
• 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. No electronic devices (calculators, phones, computers, etc).
• There will be 3 full-class exams and a final exam. There will be no make-up exams.

This course follows The University Policy on Academic Honesty .