| Course Code | COMP6741 |
| Course Title | Algorithms for Intractable Problems |
| Units of Credit | 6 |
| Course Website | http://www.cse.unsw.edu.au/~cs6741/ |
| Handbook Entry | http://www.handbook.unsw.edu.au/undergraduate/courses/current/COMP6741.html |
| Lecturer in charge | Serge Gaspers |
The course focuses on algorithms for solving intractable computational problems, so-called NP-hard problems. Ideally, one would want to design algorithms that solve each instance exactly and in polynomial time. But since no polynomial time algorithm is known for any NP-hard problem, we will relax these requirements and design algorithms that either do not solve the problem exactly, that only solve a subset of instances, or whose worst-case running time is super-polynomial in the input size or some other parameter of the input.
Among algorithms that do not solve the problem exactly, we discuss heuristics and approximation algorithms. Heuristics do not guarantee to compute optimal solutions but tend to work well in practice. Approximation algorithms give additional guarantees of the quality of computed solution as compared to the optimal solution.
Among algorithms that only solve a subset of instances, we discuss graph classes where NP-hard graph problems often become polynomial-time solvable when the input is restricted to these classes.
Among algorithms that do not run in polynomial time, we discuss exponential-time algorithms and parameterized algorithms. In exponential-time algorithms we discuss algorithmic techniques to solve NP-hard problems provably faster than brute-force in the worst case. In parameterized algorithms, a parameter k is associated with each instance and the goal is to design algorithms whose worst-case running time is fast whenever k is small. We will also see lower bounds for problems and how to rule out certain running times under various complexity assumptions.
In addition to deterministic algorithms, we discuss speed-ups if we have access to randomised algorithms or quantum algorithms.
Lectures will be prerecorded and made available to students at the beginning of each week.
The scheduled lecture slot will be used for online consultation, discussion, and assisting with solving exercises.
NP-hard problems are often at the core of the most challenging, rewarding, and lucrative computational problems in all areas of science and technology. This course will outline principled ways to approach these problems and will give students a better understanding of when and why NP-hard computational problem can be solved with reasonable resources.
After completing the course, students are able to
This course contributes to the development of the following graduate capabilities:
| Graduate Capability |
| scholarship: capable of independent and collaborative enquiry |
| scholarship: rigorous in their analysis, critique, and reflection |
| scholarship: able to apply their knowledge and skills to solving problems |
| scholarship: capable of effective communication |
| scholarship: information literate |
| scholarship: digitally literate |
| leadership: enterprising, innovative and creative |
| leadership: capable of initiating as well as embracing change |
| leadership: collaborative team workers |
| professionalism: capable of independent, self-directed practice |
| professionalism: capable of lifelong learning |
| global citizens: capable of applying their discipline in local, national and international contexts |
This course is taught by lectures with examples, and exercises that enhances problem-solving capabilities and fortifies the understanding of newly learned concepts.
The assignments further enhance problem-solving at the students' own pace.
The exam confronts students with additional problems and test their understanding of concepts and problem-solving capabilities.Assignments. The assignment mark is composed of 4 components, each worth 25% of the assignment mark.
a. Scribe. Each lecture has an associated exercise sheet, and the lecturer-in-charge assigns 2-3 students to each exercise on these sheets. These "scribes" are in charge of synthesizing the solutions to these exercises, and any relevant discussions about these exercises that we have in class. Scribes should finalize their write-ups within one week of the live discussion of the exercises and are marked based on their write-up (not based on the quality of the solution that we came up with) and how they addressed any follow-up queries. Scribes should feel free to discuss their write-up with others.
b. Assignment 1 (individual). This is an individual assignment based on course content of Week 1.
c. Assignment 2 (individual). This is an individual assignment based on course content of Weeks 2-3.
d. Assignment 3 (group). The lecturer-in-charge partitions the students into groups of about 3 students based on their performance in Assignment 1 (a group consists of students who performed similarly in the assignment). The group assignment will have an implementation component, a written report, and a presentation.
Late Assignment Submission Policy. Late submissions have their mark reduced by 5 per cent of the maximum assessment mark per day, where partial days count as full days. No submissions will be accepted 5 days (120 hours) or more after the deadline.
Exam.
The final exam is a written open-book exam.
| Assignments | 50% |
|
Final exam
|
50% |
To pass the course, the final mark, calculated as outlined above, needs to be at least 50.
If your work in this course is affected by unforeseen adverse circumstances, you should apply for Special Consideration through MyUNSW, including documentation on how your work has been affected. If your request is reasonable and your work has clearly been impacted, then
Note the use of the word "may". None of the above is guaranteed. It depends on you making a convincing case that the circumstances have clearly impacted your ability to work.
If you are registered with Disability Services, please forward your documentation to the lecturer-in-charge within the first two weeks of the term, before the first assignment is due.
The Student Code of Conduct ( Information , Policy ) sets out what the University expects from students as members of the UNSW community. As well as the learning, teaching and research environment, the University aims to provide an environment that enables students to achieve their full potential and to provide an experience consistent with the University's values and guiding principles. A condition of enrolment is that students inform themselves of the University's rules and policies affecting them, and conduct themselves accordingly.
In particular, students have the responsibility to observe standards of equity and respect in dealing with every member of the University community. This applies to all activities on UNSW premises and all external activities related to study and research. This includes behaviour in person as well as behaviour on social media, for example Facebook groups set up for the purpose of discussing UNSW courses or course work. Behaviour that is considered in breach of the Student Code Policy as discriminatory, sexually inappropriate, bullying, harassing, invading another's privacy or causing any person to fear for their personal safety is serious misconduct and can lead to severe penalties, including suspension or exclusion from UNSW.
If you have any concerns, you may raise them with your lecturer, or approach the School Ethics Officer , Grievance Officer , or one of the student representatives.
Plagiarism is defined as using the words or ideas of others and presenting them as your own. UNSW and CSE treat plagiarism as academic misconduct, which means that it carries penalties as severe as being excluded from further study at UNSW. There are several on-line sources to help you understand what plagiarism is and how it is dealt with at UNSW:
Make sure that you read and understand these. Ignorance is not accepted as an excuse for plagiarism. In particular, you are also responsible that your assignment files are not accessible by anyone but you by setting the correct permissions in your CSE directory and code repository, if using. Note also that plagiarism includes paying or asking another person to do a piece of work for you and then submitting it as your own work.
UNSW has an ongoing commitment to fostering a culture of learning informed by academic integrity. All UNSW staff and students have a responsibility to adhere to this principle of academic integrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism at UNSW is defined as using the words or ideas of others and passing them off as your own.
If you haven't done so yet, please take the time to read the full text of
The pages below describe the policies and procedures in more detail:
You should also read the following page which describes your rights and responsibilities in the CSE context:
| Week | Lectures |
| 1 |
Introduction; review of NP-completeness
|
| 2 | Kernelization; approximation algorithms; (integer) linear programming |
| 3 | Kernelization; basics of Parameterized Complexity |
| 4 | Parameterized intractability; branching algorithms |
| 5 | Branching algorithms; measure & conquer |
| 6 |
-
|
| 7 | Randomized algorithms; treewidth |
| 8 |
Treewidth; quantum algorithms
|
| 9 | Exponential time hypothesis; heuristics and local search |
| 10 | Group assignment presentations; review |
| Assignment | announced on | submit by | feedback on |
| Scribe | ongoing | within 1 week | within 1 week |
| 1 (individual) | 15 Feb | 24 Feb (5pm) | 10 Mar |
| 2 (individual) | 01 Mar | 10 Mar (5pm) | 24 Mar |
| 3 (group) |
15 Mar
|
|
21 Apr |
Recommended readings
Other useful resources
This course is evaluated each session using the myExperience system.
In the previous offerings of this course, no substantial deficiencies were notes. Students did however make helpful comments on how to improve the course.
Based on their comments, improvements have been made to the course handouts for both black-and-white and color printing, the structure of lectures, references have been given in a more detailed way, a timeline has been set for feedback on assignments, the mid-session quiz has been removed, the weight of the assignments has increased while their number has increased, then decreased again.
Resource created Friday 03 February 2023, 06:46:35 PM, last modified Friday 10 February 2023, 05:17:20 PM.