Introduction to Algorithms (Section 01, Sheldon)

Welcome to the Fall 2022 homepage for CMPSCI 311: Introduction to Algorithms. Below find basic information, coursework and schedule, and detailed course policies.

Instructor | Dan Sheldon, (email: sheldon at cs ) |

Lecture | Tuesday, Thursday 11:30–12:45pm, Goessmann Lab 20 |

Discussion | Friday 10:10–11:00am, LGRT 123 (Section 01AA) Friday 11:15am–12:05pm, LGRT 123 (Section 01AB) Friday 12:20–1:10pm, LGRT 121 (Section 01AC) |

Required Textbook | Algorithm Design, 1st edition by Jon Kleinberg and Eva Tardos |

Moodle | https://umass.moonami.com/course/view.php?id=33356 |

Gradescope | https://www.gradescope.com/courses/299373 |

Piazza | https://piazza.com/umass/fall2022/compsci31101 |

Echo 360 | https://umass.moonami.com/mod/lti/view.php?id=1810792 |

TAs | Zhipeng Tang (zhipengtang at umass.edu) Javier Burroni (jburroni at cs.umass.edu) Hie Tran (hieutran at umass.edu) Jacob Goldman (jacobgoldman at umass.edu) |

UCAs | Jacob Urisman, Animesh Saxena, Jack Champagne, Haman Bagherianlemraski, Nitya Aryasomayajula |

Office Hours | Complete list |

- Midterm 1: Wednesday, September 28 from 7–9pm in Marcus 131
- Midterm 2: Wednesday, October 26 from 7–9pm
- Midterm 3: Monday, November 21 from 7–9pm
- Final exam: Tuesday, December 20 from 1–3pm

Weekly online assignments be posted on Gradescope and due on Fridays at 11:59pm.

Challenge problem sets will be posted here and submitted on Gradescope

- Challenge Problems 1: due Wed 9/21 at 11:59pm
- Challenge Problems 2: due Wed 10/5 at 11:59pm
- Challenge Problems 3: due Wed 10/19 at 11:59pm
- Challenge Problems 4: due Wed 11/2 at 11:59pm
- Challenge Problems 5: due Wed 11/16 at 11:59pm
- Challenge Problems 6: due Wed 12/7 at 11:59pm

(**due dates tentative until posted and likely to
change**; typically posted 2 weeks before due date, plus or minus
a couple days)

Here is an approximate schedule for the course. This is subject to change and will be updated as we go. Slides will be added after class—links will be broken until they are added. Lectures may include board work that is not captured digitally. Another set of slides that roughly matches the material we cover can be found here.

Week | Date | Topic | Reading and Background | |
---|---|---|---|---|

1 | Lec 01 | 9/6 | Introduction and Stable Matching (annotated slides) | Chapter 1 |

Lec 02 | 9/8 | Algorithm Analysis | Chapter 2.1, 2.2 | |

Dis 01 | 9/9 | |||

2 | Lec 03 | 9/13 | Algorithm Analysis | Chapter 2.4 |

Lec 04 | 9/15 | Algorithm Analysis / Graphs | Chapter 3.1, 3.2 | |

Dis 02 | 9/16 | |||

3 | Lec 05 | 9/20 | Graphs | Chapter 3.3, 3.4 |

Lec 06 | 9/23 | Graphs | Chapter 3.5, 3.6 | |

Dis 03 | 9/24 | |||

4 | Lec 07 | 9/27 | Greedy | Chapter 4.1 |

Lec 08 | 9/29 | Greedy | Chapter 4.2 | |

Dis 04 | 9/30 | |||

5 | Lec 09 | 10/4 | Greedy | Chapter 4.4 |

Lec 10 | 10/6 | Greedy | Chapter 4.5, 4.6 | |

Dis 05 | 10/7 | |||

6 | Lec 11 | 10/11 | Divide and Conquer | Chapter 5.1, 5.2 |

Lec 12 | 10/13 | Divide and Conquer | Chapter 5.4, 5.5 | |

Dis 06 | 10/14 | |||

7 | Lec 13 | 10/18 | Divide and Conquer | Chapter 5.2, 5.6 |

Lec 14 | 10/20 | Dynamic Programming | Chapter 6.1, 6.2 | |

Dis 07 | 10/21 | |||

8 | Lec 15 | 10/25 | Dynamic Programming | Chapter 6.3, 6.4 |

Lec 16 | 10/27 | Dynamic Programming | Chapter 6.6 | |

Dis 08 | 10/28 | |||

9 | Lec 17 | 11/1 | Dynamic Programming | Chapter 6.8 |

Lec 18 | 11/3 | Network Flow | Chapter 7.1, 7.2 | |

Dis 09 | 11/4 | Discussion | ||

10 | Lec 19 | 11/8 | Network Flow | Chapter 7.2, 7.3 |

Lec 20 | 11/10 | Network Flow | Chapter 7.5, 7.10 | |

11/11 | No discussion — Veteran’s Day | |||

11 | Lec 21 | 11/15 | Intractability | Chapter 8.1 |

Lec 22 | 11/17 | Intractability | Chapter 8.2, 8.3 | |

Dis 10 | 11/18 | |||

12 | Dis 11 | 11/22 | Discussion (Friday schedule) | |

11/24 | No class — Thanksgiving | |||

11/25 | No discussion — Thanksgiving | |||

13 | Lec 23 | 11/29 | Intractability | Chapter 8.3 |

Lec 24 | 12/1 | Intractability | Chapter 8.4 | |

Dis 12 | 12/2 | Discussion | ||

14 | Lec 25 | 12/6 | Approximation Algorithms | Chapter 11.1, 11.2 |

Lec 26 | 12/8 | Randomized Algorithms / Review | Chapter 13.1, 13.2, 13.4 | |

Dis 13 | 12/9 | Discussion |

*(subject to change until classes begin)*

CS 187 and CS 250 are important prerequisites. These provide familiarity with basic data structures and mathematical reasoning. You should be able to program in Java, C, or a related language.

The required textbook is Algorithm Design, 1st edition by Jon Kleinberg and Eva Tardos. It will be used for readings and homework problems.

The iClicker2 student remote is required for participation in lecture and can be bought through the UMass eCampus virtual book store.

Attendance is required at lectures and discussion sections and will contribute to your participation grade. See the Participation section below for details about the participation grade and excused absences.

Students will complete:

- Weekly online homework assignments, focused on learning goal mastery
- 5–6 sets of “challenge problems”
- Three evening exams
- One final exam
- Readings
- Weekly discussion exercises

The grade percentages are as follows:

**Participation**(10%): Discussion and in-class participation (iClicker)**Homework**(10%): Weekly online assignments on Gradescope focused on learning-goal mastery**Challenge problems**: (25%): Roughly bi-weekly, focuses on algorithm design**Self-assessments**(5%): Review solutions to challenge problems and self-assess your own solutions**Test 1**(10%): Focuses on first quarter of class**Test 2**(10%): Focuses on second quarter of class**Test 3**(10%): Focuses on third quarter of class**Final**(20%): Covers all course materials

To compute the final grade, all grades will be mapped to a ten point scale and then averaged:

- Numeric grades will map linearly to 0–10; for example, a percentage grade of 93% will map to 9.3 and 68% will map to 6.8.
- Letter grades (e.g., for challenge problems) will map as follows: A+=10.0, A=9.5, B=8.5, C=7.5, D=6.5, F=5.5.

The overall average grade will be rounded to the nearest hundredth, and then grade ranges for final letter grades will be approximately: A (9.33-10.00), A- (9.00-9.32), B+ (8.67-8.99), B (8.33-8.66), B- (8.00-8.32), C+ (7.67-7.99), C (7.33-7.66), C- (7.00-7.32), D+ (6.67-6.99), D (6.00-6.66), F (0-5.99). The instructors reserve the right to adjust grade thresholds, but will not increase the minimum score required to receive any letter grade.

**Online homework assignments**should be completed independently. These are focused on mastering learning goals, and are similar to what will appear on tests. You are allowed/encouraged to ask for help from course staff or other students to learn how to solve the problems, but should eventually complete the problems on your own. Copying, sharing, or viewing any solutions that are not your own is a violation of course policy.**Challenge problems**. Collaboration is allowed. These problems take time to understand and solve, and you can benefit from developing ideas and solutions in small groups.**However, each student must write their own solutions, and no collaboration is allowed while writing the solutions.**Writing solutions on your own will cement understanding of the problem and demonstrate mastery of the solution.**Looking at solutions from other students or any other source (including the web), or collaborating to write solutions, is considered a violation of the Academic Honesty Policy.**It is easy to tell when a student has referred to solutions that are not their own.**Discussion**: Exercises during discussion sections will be completed in assigned groups.**Exams**: Closed book and no electronics.

The course staff will pursue academic honesty charges for any suspected violation of course collaboration and cheating policies.

You will receive credit for completing discussion exercises and answering iClicker questions during lectures:

- For lectures, each iClicker question during is worth 1 point, with 80% credit for participation and 20% for correctness. The first two lectures will not be counted. After that, the lowest three grades will be dropped.
- For discussions, worksheets will be submitted via Gradescope at the end of each discussion. Students will receive full credit for participation. The lowest two grades will be dropped.

In effect, this means you can miss three lectures and two discussions with no penalty.

We reserve the right to change particpation grading (e.g., to grade discussion exercises for completeness or correctness) if engagement is a problem.

To request an excused absence (e.g., for illness, conflict with recognized university activities, religious holidays, or other things beyond the student’s control), fill out this private questionnaire on Moodle. iClicker questions and discussion exercises for excused absences will be dropped when computing your average.

In the event of unforeseen disruptions, e.g., due to COVID-19, modifications to the participation policy may be announced.

Online Gradescope homework assignments will due most Fridays and posted about a week in advance. These will focus on mastery of learning goals and mimic the types of questions you can expect on exams.

These usually involve designing an algorithm for a novel problem and proving it correct. They assess your ability to apply the more concrete learning goals to solve new problems, and to use logic and language to precisely communicate your solution and justify why it is correct.

Challenge problems will be graded as one of ✗, ✓–, ✓, or ✓+ using the rubric described below. Grades of ✓ and ✓+ indicate mastery and will contribute to your homework grade as follows:

Grade | Criteria |
---|---|

A+ | Complete at least 14 challenge problems with ✓ or better; including at least 7 with ✓+ |

A | Complete at least 12 challenge problems with ✓ or better; including at least 6 with ✓+ |

B | Complete at least 8 challenge problems with ✓ or better; including at least 4 with ✓+ |

C | Complete at least 6 challenge problems with a ✓ |

D | Attempt at least 6 challenge problems and complete at least 3 challenge problems with a ✓ |

For example, to earn a C you should aim to complete one challenge problem per assignment with a ✓ or better. To earn an A, you should aim to complete two per assigment with ✓ or better with one a ✓+. Since you don’t need to complete every problem, you are encouraged to focus your efforts on producing high-quality solutions to the problems you feel confident about. There is no benefit to guessing or writing vague answers to a problem you don’t know how to solve.

This rubric is based on Mark Talbert’s EMRN rubric:

Mark | Criteria |
---|---|

✓+ | The work meets or exceeds the expectations
of the assignment. Communication is clear and complete. Mastery of the
concepts is evident. There are no non-trivial errors. This work could be
used as a classroom example. For an algorithm design
problem: the algorithm is correct and clearly communicated, the
running-time is correctly analyzed, and a convincing proof of
correctness is given. There may be minor mistakes or omissions but no
significant logic gaps. |

✓ | Understanding of the concepts is evident
through correct work and clear, audience-appropriate explanations. Some
revision or expansion is needed, but no significant gaps or errors are
present. No additional instruction on the concepts is needed.
For an algorithm design problem: the major components
of the algorithm are correct, and a running-time analysis and proof are
given. All parts of the solution are communicated in a way that a peer
who didn’t already know the solution could understand it. There may be
some logic gaps, but, on balance, the solution “hangs together”. |

✓– | Partial understanding of the concepts is evident, but there are significant gaps that remain. Needs further work, more review, and/or improved explanations. |

✗ | Not enough information is present in the work to determine whether there is understanding of the concepts. The work is fragmentary of contains significant omissions. Or, there are too many issues to justify correcting each one. |

Here is a link to a flow chart illustration of the rubric.

Challenge problems will be submitted via Gradescope. You must
**submit challenge problems as a single pdf** (see Gradescope
instructions):

- You may type your answers (e.g., using LaTeX) and save to a pdf;
- Or, you may
*neatly*write your solutions and scan them.*All scans must be high-quality*: rotated correctly, with enough contrast, and readable at a standard letter size. Please follow the Gradescope scanning guide; in particular, use a**recommended free scanning app**(typically Evernote Scannable for iOS or Genius Scan for Android). You should view the pdf once you submit to ensure it meets these standards.

Work that is not submitted in the correct format, is unreadable, or is excessively messy risks not being graded.

Intructors will post solutions to moodle 24 hours after the homework submission deadline and release the Gradescope assignment back to students for self-assessment. Each problem will be temporarily graded as “awaiting self-assessment”. Self-assessments will typically be due 3 days after the submission deadline and 48 hours after solutions are posted. For each problem attempted, you must:

- Give yourself an assessment mark, either ✗, ✓–, ✓, or ✓+, based on the rubric above.
- Provide a short reflection on why you earned that mark, such as
- “My solution was on point and very similar to the posted solution”
- “I was confused by the definition of…”
- “I incorrectly assumed that …”

- (optional) Ask specific questions to prompt instructor or TA
feedback, such as:
- “Can you check if this is actually a counterexample?”
- (indicate part of a proof you’re unsure of) “I didn’t know how to phrase this – is what I wrote on track?”

- (optional) Provide one hint for the problem (to your past self or future student)
- Submit the self-assessment by opening a regrade request on Gradescope for the problem and typing the text of your self-assessment in the text box for the regrade request. Here is a link to instructions on submitting a regrade request on Gradescope.

Late work that is not excused will receive no credit. A small grace period (on the order of 10 minutes) will generally be granted to accommodate technical issues, but it is best not rely on this.

Every student may use up to *three* “late days” to excuse late
work (either online assignments or challenge problems):

- a late day allows you to submit one assignment up to 24 hours late without penalty
**at most one late day can be used per assignment**(solutions will be posted 24 hours after the due date)

To use a late day, you do not need to notify course staff; just submit within 24 hours after the due date, and we will automatically deduct one late day from your total.

In exceptional circumstances, students may be granted extensions by the instructors. If so, it is a violation of course policies to look at posted solutions prior to submitting work.

The discussion section will be used every week except when noted on the course schedule and will consist of exercises to practice solving problems in small groups. Attendance is required.

(Numbers 2 and higher correspond to chapters in Kleinberg and Tardos.)

**Cross-Cutting**. Develop skills in abstract reasoning and communication about algorithms- Use logic to reason about algorithms
- Use self-regulated learning to solve challenging problems that require multiple cycles of planning, executing, assessment, and adaptation
- Use language, pseudocode, and mathematical notation to understand and communicate precisely about algorithms

**Basics of Algorithm Analysis**. Use asymptotic order notation (big-O, big-Omega, and big-Theta) to analyze running times and compare growth rates- Prove statements about asymptotic order notation
- Compare growth rates of different functions
- Analyze the running time of algorithms

**Graphs**. Understand graph definitions, graph traversal algorithms, and how they are used as building blocks of algorithms- Work with graph definitions and execute traversal algorithms on example graphs
- Design algorithms using graph traversal

**Greedy algorithms**. Design greedy algorithms and understand greedy proof techniques- Evaluate greedy rules for optimality
- Prove correctness of greedy algorithms
- Reason about shortest paths, cuts, cycles, and spanning trees in graphs
- Work with Dijkstra’s, Prim’s, and Kruskal’s algorithms in examples

**Divide-and-Conquer**. Understand the divide-and-conquer design technique and analyze the running-time of recursive algorithms.- Use unrolling, recursion trees, and the master theorem to solve recurrences
- Verify the solution to a recurrence using induction
- Design divide-and-conquer algorithms and argue correctness

**Dynamic Programming**. Design dynamic programming algorithms- Write a recurrence for the optimal value of a dynamic programming problem
- Translate a recurrence into an iterative algorithm to compute the optimal value
- Modify an iterative algorithm for the optimal value to recover the optimal solution

**Network Flows**. Understand network flows and use them to design algorithms- Work with cuts and flows and execute the Ford-Fulkerson algorithm in example networks
- Design algorithms to solve network flow applications

**Intractability**. Reason about intractability- Design polynomial-time reductions between pairs of problems
- Prove that a problem is NP-complete using polynomial-time reductions

- We will use Piazza for the class discussion forum and contacting instructors and TAs. [link]
- We will use Moodle for quizzes and posting HW solutions and grades. [link]
- We will use Gradescope for submitting and returning homework and exams. [link]

Please use Piazza to ask questions about course material. Use the excused absence questionnaire to request an excused absence (see the Participation section). We prefer that you use Piazza to contact instructors about other topics, but you may use email to contact us confidentially.

We will do our best to respond within 1 “business day” (i.e., a day
when classes meet). For messages received during the evening, on
weekends, or on holidays, we may respond, but please do not
*expect* a response until the next business day.

Students and course staff in CS 311 are expected comply with all university public health guidelines, to use common sense (e.g., self-monitor, stay home if sick, etc.), and be courteous to others and respect their choices. As of the start of the Fall 2022 semester, UMass is a “mask welcome campus”, and masks and strongly encouraged during the first few weeks of fall semester.

Please do not come to class (or discussions, exams, office hours, etc.) if you are at risk of infecting others:

- All lectures will be recorded and posted to Echo360; in addition, pre-recorded videos from last year covering the same material will be posted
- You can request an excused absence from any course meeting by filling out this questionnaire and explaining your reason for missing class. A credible risk of infecting others is considered a valid medical reason for an excused absence. We will not generally not request supporting documentation, but reserve the right to do so, especially is abuse of the policy is suspected. For an excused absence you will not be penalized for any missed iClicker questions, discussion exercises, etc. Work may not show up as excused in Moodle before the end of the semester.

Please read the CICS inclusivity statement, copied here:

At the Manning College of Information and Computer Sciences, we believe that you belong in computing. We welcome and value all individuals, regardless of previous computer science experience, age, citizenship, disability, sex, gender identity, military experience, political views, race, religion, or sexual orientation, while maintaining an environment that celebrates, welcomes, and honors those differences.

We’re committed to supporting all our students through their journeys in computer and information sciences–especially students from identities and backgrounds that are still underrepresented in our field. Diverse perspectives on the challenges our society faces animate our vision of Computing for the Common Good. Your insight, talents, and skills are needed to protect and improve an ecosystem that relies on the combined efforts of the greatest technical minds, and we believe your place is here.

If you have a disability and would like to request accommodations, please contact Disability Services, located in 161 Whitmore Hall, (413) 545-0892. If you are eligible, they will grant you accommodations and notify the instructors.