CS 325H: Analysis of Algorithms (Fall 2020)

Instructor: Amir Nayyeri (Office hours: Wed 3:00-4:00pm at KEC 3061)

Lectures: Tue, Thr 12:00-01:20pm in WNGR 287

Tentative topic list: Asymptotic running time analysis, Recursion, Divide and conquer, Dynamic programming, Greedy algorithms, Linear programming, Computational complexity (P and NP), Randomization*, Approximation algorithms*.

Prerequisites: CS 261; Data structures and introductory discrete mathematics, trees and graphs, data structures such as priority queues, basic proof technique including induction.

Evaluation:

• Group Assignments (60%): You are encouraged to work on in groups of up to 3 students. You do not need to work in the same group for each assignment, but you will only get credit for an assignment if your name is listed on exactly one submission. Late assignments will not be accepted without prior arrangements.
• Midterm exam (20%)
• Final exam (20%):

Resources:

• The lectures are based on Jeff Erickson's book/lecture notes. See below for specific links per lectures.
• See here for a list of other useful resources.

Announcements:

• I uploaded a set of problems on dynamic programming that we discuss in class this week.
• I uploaded a set of problems that we discuss in class this week.
• I uploaded the code template for hw1. It is slightly different from the original description in the assignment. The assignment is updated as well.
• Here are some test cases for GA1, let me know if you found incorrect answers.
• Class will be in WNGR 287 from Jan 9.
• First assignment is posted, it is due in two weeks (at 1/21).

Homework:

• Group Assignment 1; Sample Test Cases; Code Template; All Test Cases.
• Group Assignment 2; Sample Test Cases; Code Template; All Test Cases.
• Group Assignment 3; Code Template; Sample Test Cases; All Test Cases..

Lectures:

1. Tue 1/7: (1) Introduciton to recursion, recursive sorting, merge sort. (2) Recursively sorting a stack, similar to our recursive insersion sort.


2. Thr 1/9: (1) Introduciton to recursion, tiling, Hanoi tower, Fibonacci numbers. (2) Catalan number, number of monotonic paths below the diagonal and related problems.


3. Tue 1/14: (1) Asymptotic running time analysis, also see these videos by Tim Roughgaden. (2) Introduciton to recursion, quick sort, introduciton to divide and conquer.


4. Thr 1/16: Divide and conquer, median selection.


5. Tue 1/21: (1) Divide and conquer, Karastuba's multiplication. (2) Divide and conquer, closest pair of points.


6. Thr 1/23: Problem solving session: we discuss this problem set.


7. Tue 1/28: Dynamic programming, max independent set on the line, splitting a sentence.


8. Thr 1/30: Dynamic programming, longest increasing subsequence, shortest monotonic path.


9. Thr 2/4: Dynamic programming, edit distance, subset sum, shortest paths in a gird.


10. Thr 2/6: Problem solving session: we discuss this problem set.


11. Tue 2/11: Greedy Algorithms, job scheduling, Huffman codes.


12. Thr 2/13: Greedy Algorithms, Huffman codes, stable matching.


13. Tue 2/18: Basic graph algorihms, introduction, whatever first search.


14. Thr 2/21: Minimum spanning tree.


15. Tue 2/25: Problem solving session: we discuss this problem set.


16. Thr 2/27: No class; Amir is traveling.


17. Tue 3/3: Computational complexity, P/NP/coNP, NP-hardness.


18. Thr 3/5: Computational complexity, 3SAT, independent set, clique, vertex cover.


19. Tue 3/10: Computational complexity, graph coloring, subset sum.


20. Tue 2/25: Problem solving session: we discuss this problem set.