Course syllabus

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Advanced Algorithms

TDA251/DIT281, Period 2, 2021: Algorithms Advanced Course

Instructor

Assistants

  • Emil Carlsson, caremil(at)chalmers.se
  • Jeremy Pope, popje(at)chalmers.se

Announcements

  • The next re-exam submission deadline is Wednesday, 24 August. If you aim at a submission, it would be desirable to express your interest some time in advance, such that we can discuss expectations.

Teaching

Lectures: always starting on Mondays 13:15 and Thursdays 10:00, in room KC.

Compulsory assignments: they are part of the grading but also a major part of the learning process. 

Consultations: by appointment.

Lecture Notes

Numbers in parentheses are corresponding sections in the textbook. Note that not all topics appear in the textbook. The remaining schedule is always preliminary, and minor changes are always possible. Lecture notes will be added during the course.

  • Lecture 1. Approximation algorithms. Examples: Load Balancing (11.1). Center Selection (11.2). Simple unweighted Vertex Cover approximation. PDF
  • Lecture 2. Approximation algorithm for Set Cover (11.3). Pricing method - example: Vertex Cover (11.4). PDF
  • Lecture 3. Approximation scheme for Knapsack (11.8). Approximation by linear programming (11.6). PDF
  • Lecture 4. Reductions and approximation ratios. Network flows and cuts (7.1-7.3). PDF
  • Lecture 5. Bipartite Matching (7.5). Disjoint Paths (7.6). Circulations (7.7). Applications of flows: survey design (7.8). PDF
  • Lecture 6. Airline scheduling (7.9). Applications of cuts: image segmentation (7.10), project selection (7.11). PDF
  • Lecture 7. Probability recap (13.12). Randomized algorithms: Repeating a random experiment. Global Min-Cut (13.2). PDF
  • Lecture 8. Max-3-Sat (13.4). XP and FPT. Small vertex covers (10.1). PDF
  • Lecture 9. Dynamic programming on subsets. Color coding. PDF
  • Lecture 10. Dynamic programming on trees (10.2). Analysis of random splitters (13.5). PDF
  • Lecture 11. Chernoff bounds with an application to load balancing (13.9-13.10). Verifying matrix products. PDF
  • Lecture 12. Hashing and finding closest points (13.6-13.7). PDF

Compulsory Assignments

  • Assignment 1: due Thursday, 11 November, 23:59. PDF
  • Assignment 2: due Thursday, 25 November, 23:59. PDF
  • Assignment 3. due Thursday, 9 December, 23:59. PDF 
  • Home exam, due Wednesday, 12 January, 23:59. PDF 

Literature

Large parts of the course are based on selected sections from the book

Jon Kleinberg, Eva Tardos: Algorithm Design. Pearson/Addison-Wesley 2006.

However, some contents may come from various other materials, i.e., they are not in the book. It should be possible to follow the course using the Lecture Notes only, but the book may serve as supplementary material.

Learning Outcomes

See also the course plan. After the course you should

  • know in more depth some important design and analysis techniques for algorithms, in particular, ways to approach NP-complete problems,
  • to some extent be able to apply such techniques to solve new problems that may arise in various applications,
  • have some practice in recognizing connections between algorithmic problems and reducing them to each other,
  • be able to explain more complex algorithms and proofs in written form,
  • know selected topics of current research on algorithms.

Grading

Grading is based on compulsory assignments and a compulsory home exam that have equal weight. The assignments are usual problem solving exercises. In the home exam you also get some specific algorithmic problem, but it can be treated in a more essayistic form. The report will be evaluated based on depth, factual correctness, and clarity of presentation. The detailed exam problem(s) and instructions are posted in December, and the submission deadline is in the exam period in January.

We do not use any point system, but we record the feedback comments and apply the following grading criteria.

5/VG: Your solutions are correct; they really solve the given problems; they are presented in a logical order and can be followed step by step; all these steps are conclusive; all claims are weil motivated; notations are well defined. There are at most some minor weak points.
4/G: Your submissions mainly fulfill the above criteria, but there also remain noticeable errors, difficulties, or gaps.
3/G: You show a basic understanding of the topics and can manage most problems, however with substantial difficulties.
U: Insufficient understanding and fundamental difficulties in most topics.

Thus, not all exercises need to be "OK'd" in order to pass the course, but omissions can lower your grade. Feel free to ask at any time what grade you can expect based on the solutions shown so far.

There is no scheduled re-exam, but you as a Chalmers student can improve your grade later on by follow-up assignments. (Be aware that this is not merely a formality. You must really achieve an improvement that justifies the higher grade.) You can express your interest before a certain deadline, and the assignment should be finished before another deadline (to be announced). There will be two such re-exam deadlines. GU students do not have this possibility, according to GU regulations.

Rules and Policies

Read them carefully and take them very seriously.

  • Exercise deadlines are firm. Delays must be motivated before the deadlines. Unannounced late submissions will not be considered. Once you have submitted a first version before the deadline, you are allowed to resubmit at any time.
  • It is allowed, even encouraged, to discuss the exercises during the course. Also, do not hesitate to ask if you have difficulties with the exercises, or if something is unclear.
  • However, you must write your final solutions on your own, using your own words, and expressing them in the way you understood them yourself.
  • Submitting others' work in your own name is cheating! It can lead to severe consequences, in very bad cases even suspension from studies.
  • Specifically, it is prohibited to copy (with or without modifications) from each other, from books, articles, web pages, etc., and to submit solutions that you got from external persons. All sources beyond the course materials must be explicitly acknowledged.
  • You are also responsible for not giving others the opportunity to cheat. We will not investigate who copied from whom.

Submission Instructions

We do not use the Assignments feature of Canvas, but everything is done simply by mail. This system (or rather non-system) has proved, over the years, to be well suited for the pedagogical goals of this course, as it is most flexible.

  • When you describe an algorithm: Explain how and why it works, do not only provide uncommented pseudocode.
  • Be concise, avoid unnecessary additional writing. In particular, you need not prove facts that are already known from the course.
  • Respect the deadlines (see Rules and Policies). It is strongly recommended to start working when the exercises have been posted, not only when the deadline is approaching.
  • Solutions must be submitted individually (not in groups!) by email to "ptr..." The subject line must contain the course code and exercise numbers.
  • Please send only PDF attachments, no other formats. Submitting handwritten and scanned solutions is not encouraged, but if you do so, the PDF must be legible.
  • Send the entire assignment as one document, rather than a separate file for each exercise.
  • Write your name, personal number, and email address in the PDF (not only in the mail).
  • If you could not solve an exercise, submit anyway and point out precisely where you got stuck. This may help us give further hints. An even better way is to ask for help early.
  • If you get feedback on an exercise: Improve your solution accordingly and resubmit as soon as possible.
  • Please resubmit the complete solution, not only isolated answers. (It can be hard to trace them.) Moreover, it helps us if you mark the changes.
  • There is no fixed limit on the number of resubmissions. However, try and address all comments, in order to avoid long chains of incremental improvements.
  • No resubmission deadlines are set during the course. There will be only one final deadline for all resubmissions.

Further remarks: Clear technical writing, besides solving the problems, is an important aspect of the assignments. Slight formulation details can make a difference: Even if two authors had the same solution in mind, one write-up can be comprehensible and the other one not. If you think that some comments are wrong or based on misunderstandings (we are not free of mistakes!), do not hesitate to discuss your doubts. Anyway, this is part of the resubmission process.

Course summary:

Date Details Due