COMP 3804:  Design and Analysis of Algorithms


Instructor: Anil Maheshwari

OFFICE HOURS: Wednesday 10:15 to 11:45 AM in Room 5125b HP

E-mail: anil@scs.carleton.ca, WWW:http://www.scs.carleton.ca/~anil


Term: Fall 2018 Class Hours: 13:05 to 14:25  Mondays and Wednesdays in TB 360

Course-TA: 

 
Starting from the Week of Sept 10th (except the Study Break Week), please go to HP  5336
  1. Arash: Mondays 9 - 10:30 AM
  2. Fedor: Thursdays 10 - 11AM
  3. Kerry: Fridays 12:45 - 2:15 PM
  4. Yunkai: Fridays 1 - 2PM

Course Objectives:
An introduction to the design and analysis of algorithms. Topics include: divide-and-conquer, dynamic programming, linear programming, greedy algorithms, graph algorithms, NP-completeness.
(Also listed as MATH 3804.) Prerequisites: COMP 2002 or COMP 2402, COMP 2804, MATH 2007 and MATH 2108, or equivalents. Lectures three hours a week.

A bit of detailed Objectives and Contents are as follows:
Objectives:
Designing algorithms, their correctness and efficiency.
How to think about abstract computation - develop algorithmic intuition - how to attack a problem algorithmically.
Algorithmic techniques - learn key techniques (greedy, divide-and-conquer, dynamic programming, LP, ..) - which technique to use for a given problem. How to compare one algorithmic solution versus another for a problem
How to express the algorithmic solution - pseodo-code - steps - analyze - argue that it is correct - essentially how will you explain your algorithmic solutions to others?

Contents (tentatively):
Introduction: Whats an Algorithm, big-O notation, recurrence relation.
Divide and Conquer: Multiplying two n-bit integers, merge-sort, Matrix Multiplication, Median, ..
Graphs: Representation, Traversals - DFS & BFS, Shortest Paths (including A* heuristic).
Greedy Algorithms: Minimum Spanning Trees, Huffman Encodings, ...
Dynamic Programming: Edit Distance, Longest Common Sequence, ...
Linear Programming: What it is, how to express several problems as LP problems (Flow, Shortest Paths, Matching), review of simplex algorithm.
NP-Completeness: search problems, polynomial time reductions, ideas of Cooks Theorem.
Whats Next: Brief idea on how to cope with NP-Complete problems - introduction to approximation algorithms, exhaustive search and search heuristics.


Text-Book
DPV: Das, Papadimitriou and Vazirani, "Introduction to Algorithms", Mc Graw Hill 2008.
(See Papadimitriou's Websitepublisher's web-site)

There are numerous other textbooks on Algorithms and  Reference Materials

The following is the schedule for assignments and exams.


Posted On
Due Date
Marked By?

% of Total Marks

BACKGROUND QUIZ1(WINTER 2010)

Background Quiz 2 (Summer 2010)
Sept 05
Never
You

Make sure you know this material - this is minimum background required to understand the material in this course
(Warning: Less than 32% had reasonable background in previous  terms). DFW of this course is pretty close  to 50% for last several terms!

A1
PDF-File
LaTeX-File
Sep 05
Sep 24



6.25%

A2
PDF-File
LaTeX File
Sep 26
Oct 15


6.25%
A3
PDF-File
LaTeX-File
Oct 31
Nov 19


6.25%
A4
PDF-File
LaTeX-File
Nov 14
Dec 05


6.25%
Mid-Term
Oct 29



25%

Final Exam
Please check exam schedule



50%


To pass this course:
  1. You must secure at least  50% Marks in the FINAL EXAM.
  2. You must secure at least a total of 50% marks in the whole course.



Fall 2018 Class-Wise Schedule:

Sep 05: Introduction to Algorithmic Thinking (Design &  Analysis of Algorithm) Illustrated via finding a subarray of an array that has the largest sum (Also see my rough draft)

Sep 10: Algorithmic Technique: Divide-and-Conquer: Vrahanka/Fibonacci numbers; How to multiply two n-bit numbers. Solving recurrences of type T(n)=aT(n/b)+f(n).
Sep 12: More on solutions of some of the standard recurrences including Multiplication, Matrix Multiplication, Merge Sort, Binary Search, etc.. Substitution method for solving recurrences of the form T(n)=T(n/3)+T(2n/3)+n=O(n log n).

Sep 17: Algorithm for finding the median element.
Sep 19: Finishing Analysis for finding the k-th order/median element. My Notes on Median. Introduction to Graphs and how to store them in
computer.

Sep 24: Intro to Graphs and Graph Traversal using depth first search
(See Chapter 3 of the textbook for details.)
Sep 26:
A1 Due. Graph traversal of undirected and directed graphs using depth first search - concept of pre and post number and its applications. 
 
Oct 01: Strongly-Connected Components - DAGs of SCC Components - G^R and G  (Section 3.4 of the textbook)
Oct 03: SCC Analysis. MST (Section 5.1)

Oct 10:
MST - Kruskal + Prim's Algorithm for MST + Associated Data Structures.
 
Oct 15:
A2 Due; Finishing Kruskal's algorithm; Heap Data Structure with Extract-Min and Decrease Key; Prim's Algorithm
Oct 17: MST-Pseudocodes. Continue with Prim's Algorithm; Some selected exercises from Assignment 2.

Oct 29:
MID-TERM [All the material covered in the course up to the Oct 17th class]
Oct 31:
SSSP -

Nov 05:
Dijkstra's Algorithm- Correctness. My Notes
Nov 07: Shortest Paths in DAGs, Increasing Sequence and Introduction to Dynamic Programming - Short and Long Paths in DAGs, Longest Increasing SubSequence [See Chapter 6 of Text Book]

Nov 12: 
DP - Matrix Multiplication, Longest Common Sequence,
Nov 14:  DP -
LCS, Knapsack, All Pairs SP.

Nov 19:
A3 Due, DP, and Intro to NP-Hardness [Richard Karp Video]
              Decision Problems,  P & NP, P \subset NP.

Nov 21:
NP-Hardness [Chapter 8] Classes P & NP-Complete, Polynomial Time Reducibility, 3CNF-SAT to CLIQUE
 
Nov 26: 
 NP-Completeness Proofs: Circuit-SAT to SAT, SAT to 3CNF-SAT, 3CNF-SAT to 0-1 ILP
Nov 28: 
NP-Hardness: 3CNF-SAT to 0-1 ILP contd., 3CNF-SAT to SUBSET-SUM, 

Dec 03:
NP-Completeness Proofs: Equivalence of Vertex-cover, Clique, Independent-Set Problems, SUBSET-SUM to Knapsack.
Dec 05: A4 Due. NP-Hardness
          
Review, Solutions to selected Exercises from Assignment 3+4,  and some remarks on Final Exam.


Dec 10: If you want, you may bring a non-programmable calculator for the final exam.
Final Exam at 2PM most likely in the Field House - Please find this out through the Carleton Exam Website.
The exam is based on the material covered in the class from Sept 5-Dec 5 (inclusive), relevant sections of the textbook, and all the assignments. Please review Assignments & exercises (solved and unsolved) in the textbook as part of preparation for the exam. The format of the exam is

- 20 Short Answer Questions worth a total of 70 = 3.5 x 20 Marks

- 2 Long Answer Questions worth a total of 30= 15 x 2 Marks.  


     


Undergraduate Academic Advisor:

The undergraduate advisor for the School of Computer Science is available in Room 5302C HP, by telephone at 520-2600, ext. 4364 or by email at undergraduate_advisor@scs.carleton.ca. The advisor can assist with information about prerequisites and preclusions, course substitutions/equivalencies, understanding your academic audit and the remaining requirements for graduation. The undergraduate advisor will also refer students to appropriate resources such as the Science Student Success Centre, Learning Support Services and the Writing Tutorial Services.
University Policies:

Student Academic Integrity Policy: Every student should be familiar with the Carleton University student academic integrity policy. A student found in violation of academic integrity standards may be awarded penalties which range from a reprimand to receiving a grade of F in the course or even being expelled from the program or University. Some examples of offences are: plagiarism and unauthorized co-operation or collaboration. Information on this policy may be found in the Undergraduate Calendar.

Plagiarism: As defined by Senate, "plagiarism is presenting, whether intentional or not, the ideas, expression of ideas or work of others as one's own". Such reported offences will be reviewed by the office of the Dean.

Unauthorized Co-operation or Collaboration:
We will follow the normal policies of Carleton University for providing academic accommodations as deemed necessary. Please contact the appropriate authorities well in advance so that you can be accommodated.

Equity Statements:
You may need special arrangements to meet your academic obligations during the term. For an accommodation request the processes are as follows:

Pregnancy obligation: write to me with any requests for academic accommodation during the first two weeks of class, or as soon as possible after the need for accommodation is known to exist. For more details visit the Equity Services website: http://www2.carleton.ca/equity/

Religious obligation: write to me with any requests for academic accommodation during the first two weeks of class, or as soon as possible after the need for accommodation is known to exist. For more details visit the Equity Services website: http://www2.carleton.ca/equity/

Academic Accommodations: The Paul Menton Centre for Students with Disabilities (PMC) provides services to students with Learning Disabilities (LD), psychiatric/mental health disabilities, Attention Deficit Hyperactivity Disorder (ADHD), Autism Spectrum Disorders (ASD), chronic medical conditions, and impairments in mobility, hearing, and vision. If you have a disability requiring academic accommodations in this course, please contact PMC at 613-520-6608 or pmc@carleton.ca for a formal evaluation. If you are already registered with the PMC, contact your PMC coordinator to send me your Letter of Accommodation at the beginning of the term, and no later than two weeks before the first in-class scheduled test or exam requiring accommodation (if applicable). Requests made within two weeks will be reviewed on a case-by-case basis. After requesting accommodation from PMC, meet with me to ensure accommodation arrangements are made. Please consult the PMC website (www.carleton.ca/pmc)  for the deadline to request accommodations for the formally-scheduled exam (if applicable).

Medical Certificate: The following is a link to the official medical certificate accepted by Carleton University for the deferral of final examinations or assignments in undergraduate courses. To access the form, please go to http://www1.carleton.ca/registrar/forms/


Announcements
  1. All announcements will be posted here or mentioned in the class - its up to you to ensure that you are up-to-date in terms of whats going on
  2. For NP-Completeness you may like to visit some of the following references:
    1. A List of NP-Complete Problems
    2. Some reductions illustrated nicely 1 2 3
    3. NP-Completeness Column
    4. Graph of NP-Complete Problems
    5. Puzzles are NP-Complete
    6. The Girl who proved P=NP
    7. Here are the lists of proofs that P=NP as well as proofs that P<>NP
    8. Here is the description from Clay Mathematical Institute
    9. Richard Karp Video
  3. Assignment 1 is posted
  4. You can upload a scanned copy of your Assignment on cuLearn. It doesn't have to be typed as such. Use a good image capturing device and upload the pdf files.
  5. Assignment 2 is posted
  6. Assignment 3 is posted
  7. Assignment 4 is posted
  8. Please try to complete the online teaching evaluation.

http://www.scs.carleton.ca/~maheshwa