CMSC451: Design and Analysis of Computer Algorithms

CMSC451 is a traditional upper-level course focused on the design and analysis of algorithms. The course presents fundamental techniques for designing efficient algorithms, proving their correctness, and analyzing their performance. Topics we will cover include:

• divide and conquer
• greedy algorithms
• dynamic programming
• graph algorithms (search, matchings, network flow)
• approximation algorithms
• randomized algorithms
• computational intractability
• algorithm design in other models of computation (parallel, quantum)

Location: CSI 2117

Section 0101 (Aravind Srinivasan): TuTh, 11am – 12:15pm

Section 0201 (Laxman Dhulipala): MW, 2pm – 3:15pm

News

• Please join the Piazza forum for this course and check that you can access Gradescope well in advance of the due date of the first assignment.

Schedule

• 1. T/TH: August 30; M/W: August 29 — Course Overview and Introduction
  • Textbook Reading: Chapter 1 of Kleinberg and Tardos
  • Understanding Science Through the Computational Lens by Richard Karp (link)
  • Chapter 20 of Mathematics + Computation by Avi Wigderson (link)
  • Short Reference Guide for 451 by Dave Mount (link)
• 2. T/Th: September 1; M/W: August 31 — Example: Stable Matching [A1 out on 8/30]
  • Textbook Reading: Chapter 1 of Kleinberg and Tardos
  • Stable matching: Theory, evidence, and practical design (Nobel Prize Citation) (link)
  • The Power of the Digi-Comp II by Scott Aaronson (link)
  • A Stable Marriage Requires Communication by Gonczarowski et al. (link)
• 3. T/Th: September 6; M/W: September 7 — Math Background
  • Textbook Reading: 2.1–2.4 of Kleinberg and Tardos
  • Short Reference Guide for 451 by Dave Mount (link)
  • Additional Notes on Induction (link)
• 4. T/Th: September 8; M/W: September 12 — Breadth-First Search, Bipartiteness, Connectivity
  • Textbook Reading: 3.1–3.5 of Kleinberg and Tardos
• 5. T/Th: September 13; M/W: September 14 — DFS, Topological Sorting [A1 due Sep 14, A2 out]
  • Textbook Reading: 3.6 of Kleinberg and Tardos
• 6. T/Th: September 15; M/W: September 19 — More Graph Algorithms
  • Textbook Reading: Chapter 3 of Kleinberg and Tardos
  • Additional Notes on Graphs (link)
• 7. T/Th: September 20; M/W: September 21 — Greedy Algorithms: Shortest Paths and MSTs
  • Textbook Reading: 4.1, 4.4, 4.5 of Kleinberg and Tardos
• 8. T/Th: September 22; M/W: September 26 — Greedy Algorithms: Scheduling
  • Textbook Reading: 4.2 of Kleinberg and Tardos
• 9. T/Th: September 27; M/W: September 28 — Divide-and-Conquer: Closest Points [A2 due Sep 28, A3 out]
  • Textbook Reading: 5.1, 5.2, 5.4 of Kleinberg and Tardos
• 10. T/Th: September 29; M/W: October 3 — Divide-and-Conquer: Polynomial Multiplication and FFT
  • Textbook Reading: 5.5, 5.6 of Kleinberg and Tardos
• 11. T/Th: October 4; M/W: October 5 — Divide-and-Conquer: Parallel Algorithms
  • Textbook Reading: Sections 1–4 of Introduction to Parallel Algorithms
• 12. T/Th: October 6; M/W: October 10 — Dynamic Programming: Weighted Interval Scheduling
  • Textbook Reading: 6.1, 6.2 of Kleinberg and Tardos
• 13. T/TH: October 11; M/W: October 12 — Dynamic Programming: Knapsack [A3 due Oct 12, A4 out]
  • Textbook Reading: 6.4 of Kleinberg and Tardos
• 14. T/Th: October 13; M/W: October 17 — Dynamic Programming: Sequence Alignment
  • Textbook Reading: 6.6 of Kleinberg and Tardos
• 15. T/Th: October 18; M/W: October 19 — Dynamic Programming: Negative-Weight Shortest Paths
  • Textbook Reading: 6.8 of Kleinberg and Tardos
• 16. T/Th: October 20; M/W: October 24 — Dynamic Programming Continued [A4 due Oct 24]
  • Textbook Reading: Chapter 6 of Kleinberg and Tardos
• T/Th: October 25; M/W: October 26 — Midterm
  • Make sure to attend your section’s exam (T/Th is Section 101, M/W is Section 201)
• 17. T/Th: October 27; M/W: October 31 — Network Flow: Ford-Fulkerson [A5 out Oct 31]
  • Textbook Reading: 7.1, 7.2 of Kleinberg and Tardos
• 18. T/Th: November 1; M/W: November 2 — Network flow: Bipartite Matching
  • Textbook Reading: 7.5 of Kleinberg and Tardos
• 19. T/Th: November 3; M/W: November 7 — Complexity: P, NP, reductions
  • Textbook Reading: 8.1, 8.2 of Kleinberg and Tardos
• 20. T/Th: November 8; M/W: November 9 — NP-completeness
  • Textbook Reading: 8.3, 8.4 of Kleinberg and Tardos
• 21. T/Th: November 10; M/W: November 14 — NP-complete Problems
  • Textbook Reading: 8.5–8.8 of Kleinberg and Tardos
• 22. T/Th: November 15; M/W: November 16 — Approximation Algorithms: Load Balancing
  • Textbook Reading: 11.1 of Kleinberg and Tardos
• 23. T/Th: November 17; M/W: November 21 — Approximation Algorithms: Set Cover [A5 due Nov 17, A6 out]
  • Textbook Reading: 11.3 of Kleinberg and Tardos
• 24. T/Th: November 22; M/W: Recorded — Randomized Algorithms: Min-Cut
  • Textbook Reading: 13.2 of Kleinberg and Tardos

• 25. T/Th: November 24; M/W: November 28 — Randomized Algorithms: Game Tree Evaluation

• 26. T/Th: November 29; M/W: November 30 — Quantum Algorithms

• 27. T/Th: December 1; M/W: December 5 — TBA [A6 due Dec 5, Final Practice out]

• 28. T/Th: December 6; M/W: December 7 — TBA

• 29. T/Th: December 8; M/W: December 12 — Final Review

Textbook and Related Resources

The required textbook is Algorithm Design by Kleinberg and Tardos. We may also occasionally use, among others, the following excellent publicly-available resources:

• Kevin Wayne’s lecture notes from Princeton
• Jeff Erickson’s Algorithms book from Urbana-Champaign
• Avrim Blum, Anupam Gupta, and Danny Sleator’s lecture notes from Carnegie-Mellon

We will sometimes add links to other useful resources which provide additional context or further investigation of the problems discussed in lecture to the Schedule.

We thank the authors for these very helpful resources.

Course Format and Grading

There will be a combination of written homeworks (about six), a midterm exam, and a comprehensive final exam.

All homework is to be done individually, but discussions with classmates are encouraged: just list the classmates you discussed the assignment with.

Please ensure that you typeset your homework in LaTeX. You can find many templates online, and here is one.

There are two sections of the course, one taught by Aravind and the other by Laxman. We will use the same homeworks for both sections, but the content of the midterm and final exam will be different. Therefore, we recommend attending the lectures for your section.

Final grades will be calculated as:

• 35% homework (lowest homework dropped)
• 25% midterm
• 40% final

Homeworks are to be turned in at the start of class on the due date. Since homework solutions will be handed out on the day the homework is due, no late homeworks will be accepted. You can discuss homeworks with other students, but with no help from the Web or other sources. Assignments are to be written up independently by each student, regardless of collaboration. If you have questions, please talk to the TA or the Instructor. It is your responsibility to make sure that you pick up all homeworks and handouts. All course information and handouts will be available on Piazza and Canvas.

Course Organization

• Announcements, discussion, and assignments posted on Piazza
• Assignment submission and feedback on Gradescope
• Office hours in-person; details below.

Prerequisites

CMSC 351. You should be familiar with discrete mathematics (induction, sets, combinatorics, probability), data structures (lists, queues, stacks, graphs, heaps), sorting algorithms, and some basic graph algorithms (Dijkstra’s algorithm, minimum spanning trees, graph search). If you have any questions about the background material, please reach out to the instructors.

Mask Policy

We will follow the masking and health guidelines laid out by the University. Note that masking is still recommended: “Effective Monday, August 29, wearing a mask will not be required while indoors in most situations, including classrooms. However, wearing a KN95 mask is recommended while indoors for added protection.”

Our Pledge to the Students

Your education is very important to us, and we respect each of you regardless of how you do in the class. Our expectations of you are that you attend class and pay full attention, and give enough time to the course. We strongly encourage you to ask questions in class, and to come to the office hours (the instructors’ or the TAs’) with any further questions. We can have a very enjoyable educational experience if you pay attention in class, give sufficient time to our course, and bring any difficulties you have promptly to our attention. We look forward to our interaction both inside and outside the classroom.

Instructors

Aravind Srinivasan. Office hours: Tuesday and Thursday 2–3PM, Location: IRB 4164, additionally by appointment

Laxman Dhulipala. Office hours: Monday and Wednesday 3:30–4:30PM, Location: IRB 5150, additionally by appointment

Teaching Assistants

Unless announced otherwise, hours will be held in IRB 2207 Open Area (the open area across from IRB 2207).

Dhruva Sahrawat. Office hours: Wednesday and Saturday 12–1pm, Location: Zoom (please see Piazza)

Keivan Rezaei. Office hours: Tuesday and Thursday 5–6pm

Kishen Gowda. Office hours: Tuesday and Friday 4–5pm

Yunheng Han. Office hours: Monday and Friday 1–2pm

Academic Accomodations for Disabilities

Any student eligible for and requesting reasonable academic accommodations due to a disability is requested to provide, to the instructor in office hours, a letter of accommodation from the Office of Disability Support Services (DSS) within the first two weeks of the semester.

Web accessibility