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Parameterized Algorithms (SS 2015)

Course Description

It is a (sad) empirical fact that most computational problems that are motivated by real-life problems are (at least!) NP-hard. So they cannot—using current algorithmic technology—be solved exactly within "reasonable" time bounds. How do we cope with this pervasive (and seemingly inescapable) hardness?

In this course, we introduce you to a very successful approach for solving hard problems fast: parameterized algorithms. The primary motivation for this approach is the observation that the computational hardness of many hard problems can be "isolated" to one or more aspects or parameters of the problem. During the course, we will explore algorithmic and structural techniques that can take advantage of this observation. In particular, we will discuss:

  1. Parameterized Algorithms: algorithms whose running times are exponential only in the chosen parameter, and are polynomial in the instance size. If the parameter is "small" in real-life inputs, then this leads to fast exact algorithms that work well in practice.
  2. Kernelization Algorithms: algorithms that reduce the size of the problem to a (hopefully small) function of the parameter. This provides a theoretical framework to understand the power of preprocessing heuristics.
  3. Hardness: How can we prove that certain problems do not have a parameterized or kernelization algorithm for a particular parameter?

Parameterized Algorithms is a very lively field of current research.

Basic Information

Lectures Tuesdays and Thursdays, 10:00-12:00
Tutorials Thursdays 16:00-18:00
Location E1.4 Room 021
Lecturers Erik Jan van Leeuwen and G Philip
Course Language English
Course Mailing List For announcements and discussion. If you want to follow the course, you should join this list. If you want to credit the course, you must join the mailing list on or before April 30, 2015.
Prerequisites The course assumes that you are familiar with algorithms, complexity, and graphs.
At Saarland University, these fundamentals are taught mostly in the course Grundzüge von Algorithmen und Datenstrukturen (Algorithms and Data Structures) and some also in the course Grundzüge der Theoretischen Informatik.
Literature You do not need to buy a book for this course. Instead, you are expected to make notes during the lectures. However, the content of this course is based on four recent books on parameterized algorithms, that you can find in the library.
Credits 6 credits, graded
Assignments There will be three sets of assignments to hand in. Each set accounts for 10% of the final grade.
Examination The course has two exams: one mid-semester test and one final exam. The mid-semester test accounts for 30% of the final grade, the final exam for the remaining 40%. You can only take part in the final exam if you have done the mid-semester test.
Re-exam There will be a possibility for a re-exam of the final exam. You can only take part in the re-exam if you have done the mid-semester test.
Exam Dates Mid-term: Tuesday, June 16, 09.00 - 12.00, E1.4 Room 021.
Final exam: Tuesday, August 4, 9.00 - 12.00, E1.4 Room 021.
Re-exam: Tuesday, September 22, 09.00 - 12.00, E1.4 Room 021.


Note that the schedule is dense during the first half of the semester, and not so much during the second half.
Topics on future dates are tentative.

21 AprIntroduction
23 AprBranchingTutorial
28 AprIterated Compression
30 AprColor CodingTutorial
5 MayImportant Separators
7 MayTutorialAssignment I
12 MayAssignment I
14 MayNo class: Ascension
19 MayTreewidth I
21 MayTreewidth IITutorial
26 MayGraph Minors I
28 MayGraph Minors IITutorial
2 JunAssignment II
4 JunNo class: Corpus ChristiAssignment II
9 JunKernelization I
11 JunTutorial
16 JunMid-Semester Test
18 JunTutorial
23 Jun
25 Jun
30 Jun
2 JulKernelization II
7 Jul
9 JulKernelization IIITutorial
14 JulLower Bounds I
16 JulTutorialAssignment III
21 JulAssignment III
23 JulLower Bounds IITutorial
28 Jul
30 JulLower Bounds IIITutorial

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