- Peter Damaschke, ptr(at)chalmers.se, EDIT 6478. (Use the correct mail address. Do not add "student" by mistake.)

Email: add "(at)chalmers.se", unless said otherwise.

- Emil Carlsson (caremil)
- Ivan Oleinikov (ivanol)
- Niklas Åkerblom (niklas.akerblom)
- Yu Zheng (zhyu)

Doing part of the assignment grading only. Email: add "(at)student.chalmers.se", unless said otherwise.

- Qufei Wang (qufei)
- Johanna Warnqvist (johwar)
- Maria Kokkou (kokkou)

- Ebrahim Mohammadi (ebrmoh(at)student.chalmers.se)
- Erik Brorsson (erikbro(at)student.chalmers.se)
- Daniel Willim (willim(at)student.chalmers.se)
- Yvonne Hansson (gushansyv(at)student.gu.se)
- Robin Karhu (guskempro(at)student.gu.se)
- Vibha Satyam (gussatyvi(at)student.gu.se)

- This is an auxiliary course home page besides the Canvas page. Some materials are only in Canvas, but not here.
- More advice (updated 6 Oct.).
- The re-exam will be in March 2021, and it is identical to the regular exam of the course edition in period 3, 2021. (We emphasize this, because there have been erroneous announcements of the re-exam date on other pages.)

Some old exams: 2020 (Aug.) 2019 2018 2017 2016 2015

For the sake of efficient support and proper scheduling of the exercises, we assume that you study each part of the Lecture Notes until the date when the lecture normally would have been scheduled.

Do not hesitate to send many emails (primarily to the instructor) about any questions you need help with. The time freed by not giving lectures is available for more extensive help - please make use of this resource.

Online exercise sessions: see the Canvas page.

Numbers indicate the related book sections. (Note: Chapters have different numbers in some editions of the book, in particular, chapters 4 and 5 are swapped. But it should be easy to recognize this and find the correct chapters by their titles anyway.) Sections with the label "Problem" describe the computational problems treated in the course; do not misunderstand them as exercises.

**Lecture 1.**General notions: problem, instance, algorithm. Time complexity and O-notation (2.1, 2.2, 2.4). PDF.**Lecture 2.**Greedy algorithms. Interval Scheduling (4.1). PDF.**Lecture 3.**Dynamic programming. Weighted Interval Scheduling (6.1, 6.2). PDF.**Lecture 4.**Dynamic programming for: Subset Sum and Knapsack (6.4). Segmentation problems (6.3). PDF.**Lecture 5.**Dynamic programming for Sequence Alignment (6.6). Divide-and conquer. Binary search (end of 2.4). Skyline problem. PDF.**Lecture 6.**Recurrences (5.1-5.2). Briefly about Sorting and Median Finding (5.1, 13.5). PDF.**Lecture 7.**Counting Inversions (5.3). Fast Multiplication (5.5). Polynomial-time reductions (8.1). PDF.**Lecture 8.**Complexity classes P and NP (8.3). NP-completeness (8.4). Satisfiability problem (8.2). PDF.**Lecture 9.**Several NP-complete problems (from 8.5-8.7, very cursory). PDF.**Lecture 10.**Graph traversal and Connectivity (3.2, 3.5). Coloring and Bipartiteness (3.4). PDF.**Lecture 11.**Minimum Spanning Tree (4.5). Directed cycles and Topological Order, DAGs (3.6). PDF.**Lecture 12.**Shortest and longest paths in DAGs and general graphs. Union-and-Find (4.6). Interval Partitioning (end of 4.1). Space-efficient Sequence Alignment (6.7). PDF.**Lecture 13.**Closest points (5.4). Clustering with maximum spacing (4.7). PDF.

Here we list some particularly recommended exercises from the book, for those who want to practice a bit more on their own. You are also welcome to send questions about them.

- Greedy (chapter 4): 3 (loading trucks), 4 (subsequence), 5 (base stations on a road), 7 (assign jobs to computers), 13 (minimize the sum of weighted completion times), 17 (circular Interval Scheduling)
- Dynamic programming (chapter 6): 2b (low and high stress), 4c (business in two cities), 6 (pretty printing), 17 (rising trend)
- Searching and divide-and-conquer (chapter 5): 1 (median of two sets), 2 (significant inversions), 3 (equivalent majority), 5 (hidden surface removal)
- Reductions and NP-completeness (chapter 8): 1 (reducible or not), 2 (diversity), 3 (qualified counselors), 5 (hitting set), 6 (monotone SAT), 14 (multiple interval scheduling)
- DAGs (chapter 3): 3 (order or cycle), 12 (consistent historical data)
- Proving some graph properties (chapter 3): 5 (number of nodes in a tree), 7 (high degree implies connectivity),

Times for weekly exercise meetings: see Announcements section.

The course follows selected parts of the textbook

Jon Kleinberg, Eva Tardos: *Algorithm Design.* Pearson/Addison-Wesley 2006, ISBN 0-321-29535-8.

See also the syllabus in the Student Portal.

The course provides basic knowledge and methods for the design and analysis of fast and correct algorithms that solve new problems with the use of computers. The intuitive notion of time complexity is applied in a strict sense. After completion of this course, you should be able to:

- describe algorithms in writing, prove that they are correct and fast,
- recognize non-trivial computational problems in real-world applications and formalize them,
- recognize computationally intractable problems,
- apply the main design techniques for efficient algorithms to problems which are similar to the course examples but new,
- perform the whole development cycle of algorithms: problem analysis, choosing, modifying and combining suitable techniques and data structures, analysis of correctness and complexity, filling in implementation details, looking for possible improvements, etc.,
- perform simple reductions between problems,
- explain on a technical level what NP completeness means,
- critically assess algorithmic ideas,
- explain why time efficiency and correctness proofs are crucial.

This is not a course in programming! The main focus is on the analytical work that has to be done before writing any line of code. Accordingly, the implementation of algorithms is NOT practiced here.

**Grades** are based on the points in the written exam. Point limits for the grades 3, 4, 5 and G, VG will be announced there.

Course plan Chalmers

Course plan GU

*"Tell me and I forget. Show me and I remember. Let me do and I understand." (attributed to Confucius) *

Computational problems in practice rarely occur in nice textbook form. We must be able to apply general algorithm design techniques to **new problems**, or at least adapt and adjust known algorithms to new variants of known problems. **Therefore this course is problem-oriented** and the exam will require problem solving, too.

Moreover, one cannot learn these skills just by listening, or by reading a lot of solutions written by others. (Compare to other skills: One cannot learn to play a musical instrument just be watching others playing. Of course, one has to practice!) It is important to invest own work and **actively solve problems**. The course offers possibilities for that, mainly by doing **assignments**.

While the assignments are **voluntary**, it is **strongly recommended** to work on them as much as you can. Then you will be in a much better position in the exam, but we also hope that you work on them because you find them interesting as such.

**Written solutions to assignments:**

Most importantly, train your ability to communicate solutions in written form. Even when you have solved an exercise and the solution seems clear to you, comprehensible writing remains a challenge. Moreover, **in the exam you must do it** - and you want the graders to understand your solutions. We advise you to **submit written solutions to the assignments,** as many as you can. The deadline is always **Sunday 23:59.** (Of course, you may submit earlier.) All assignments shall be done individually. Discussion is encouraged, but what you submit must be written in your own words and reflect your own understanding. Submission details: see below.

We use the Fire submission system rather than the Assignments feature of Canvas.

Make sure that you use only the link to Fire provided here, not a link from an earlier year.

First create an account in Fire. You do this only **once**. As all assignments are individual, you don't have to create a group in Fire.

**To create an account:** Go to the submission system. Bookmark the link (you will need it again), click on "Click here to register as a student" and fill in your email address (preferably your student address). You will get a mail with a web address. Click this address, it leads you to a page where you can fill in your data: name, personal number, and a password. Spell your name correctly as "Firstname Surname" (only the most commonly used first name is needed, with big initial letters) and write your personal number as yymmdd-xxxx with the dash, i.e., the minus sign. Log on using the account you have just created.

**To submit a solution:** Log on to Fire again. Upload the file(s) that make up your solution. Finally press the "submit" button. (This is easy to forget.) Fire will close exactly at the given deadlines, therefore, do not wait until the last minute.

Solutions should be submitted as PDF files, created with a word processor or latex or by scanning handwritten sheets - provided that they are readable. Your files must contain your name. Send a separate file for each problem.

From the grader you will receive a mail with comments. You can also download the comments from Fire.

**Special remark:** By default you may always get "fail"; this has only technical reasons (possibility to resubmit an improved solution) and does not mean anything. Only the comments are of interest.