Algorithmic Combinatorics

Winter 2018-19

FU Berlin, Mathematics and Informatics



Many thanks to Toptal for this animation.

Course Details

Listed below are the administrative details regarding the course.

Schedule

There will be two lectures every week, as detailed below.

Lectures: Tuesdays from 14:30 to 16:00 in Takustrasse 9, SR 46 and Wednesdays from 12:30 to 14:00 in Arnimallee 6, SR 7/8.

You are also encouraged to attend one of the following exercise classes.
(We won't stop you from attending both if you really want to.)

Exercises: Tuesdays from 16:15 to 18:00 in Takustrasse 9, SR 6 and Thursdays from 10:30 to 12:00 in Arnimallee 6, SR 31.

Instructors

Tibor Szabó
Arnimallee 3, Room 211a

Anurag Bishnoi
Arnimallee 3, Room 206

Office hours are by appointment, so please e-mail as needed.

Exams and Requirements

The final grade for this course will be from a written exam. The first exam will be held on Wednesday, February 20th, from 1 pm to 4 pm

The second exam will be held on April 2nd, from 1 pm to 4 pm.

The full set of requirements and formalities for the course can be found here.

Credits

Master's students at the Freie Universität Berlin may take this course either as
"Diskrete Mathematik II" or as an Ergänzungsmodul.

Phase I students from the Berlin Mathematical School may take this course as the basic course "Discrete Optimization" in teaching area 4.

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Topics

We shall explore the use of algorithms in combinatorics. The main topics will be:

References

The following texts are recommended for this course.

The interested reader might also enjoy the following.

Prerequisites

This course is a second course in the Discrete Mathematics module, and we assume our students are familiar with the basic concepts of graph theory and combinatorics covered in the Discrete Mathematics I course (see here for the relevant material).

We will also make use of undergraduate linear algebra, calculus and probability.

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Exercises

There will be a homework assignment you should solve in pairs.

Submit your solutions by the end of the Tuesday lecture, either in class itself, or to the tutor box of Anurag Bishnoi.

Quiz Homework Due date Comments
Week 0 Sheet 0 Never To be discussed on 16/10
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Course Progress

Topics

As we make our way through the semester, we will provide below a brief review of the topics covered each week.

Lecture Topics References
1 Sorting algorithms: (Binary) insertion sort, Mergesort; Analysis: running time, matching lower bound
2 Spanning trees: Depth-first and breadth-first search, Kruskal's algorithm for minimum-weight spanning trees LPV 9.1
West 2.3