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FI:MA015 Graph Algorithms - Course Information

## MA015 Graph Algorithms

**Faculty of Informatics**

Autumn 2019

**Extent and Intensity**- 2/1/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
**Teacher(s)**- doc. Mgr. Jan Obdržálek, PhD. (lecturer)

RNDr. Bc. Dominik Velan (seminar tutor) **Guaranteed by**- doc. Mgr. Jan Obdržálek, PhD.

Department of Computer Science - Faculty of Informatics

Supplier department: Department of Computer Science - Faculty of Informatics **Timetable**- Wed 12:00–13:50 A217
- Timetable of Seminar Groups:

*D. Velan*, Rezerva, nepřihlašuje se.

MA015/R4: each odd Tuesday 10:00–11:50 C511,*D. Velan*, Rezerva, nepřihlašuje se.

MA015/01: each even Tuesday 16:00–17:50 B410,*J. Obdržálek*

MA015/02: each odd Tuesday 16:00–17:50 B410,*J. Obdržálek* **Prerequisites**-
**MB005**Foundations of mathematics ||(**MB101**Mathematics I &&**MB102**Calculus )||(**MB201**Linear models B &&**MB102**Calculus )||(**MB101**Mathematics I &&**MB202**Calculus B )||(**MB201**Linear models B &&**MB202**Calculus B )||(**PřF:M1120**Discrete Mathematics )|| PROGRAM ( N - IN )|| PROGRAM ( N - AP )

Knowledge of basic graph algorithms, to the extent covered by the course IV003 Algorithms and Data Structures II. Specifically, students should already understand the following datastructures and algorithms: Graphs searching: DFS, BFS. Network flows: Ford-Fulkerson, Golderg (push-relabel). Minimum spanning trees: Boruvka, Jarnik (Prim), Kruskal. Shortest paths: Bellman-Ford, Dijkstra. Datastructures: heaps (incl. Fibonacci), disjoint set (union-find), ... **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- there are 26 fields of study the course is directly associated with, display
**Course objectives**- The course introduces graph important algorithms beyond the reach of standard algorithms and data structures courses. Covered algorithms span most of the important application areas of graphs algorithms.
**Learning outcomes**- At the end of the course students will under know and understand important graph algorithms beyond the reach of standard algorithms and data structures courses. Covered algorithms span most of the important application areas of graphs algorithms. The students also should be able to choose an algorithm best suited for a given task, modifying it when necessary, and estimate its complexity.
**Syllabus**- Minimum Spanning Trees. Quick overview of basic algorithms (Kruskal, Jarník [Prim], Borůvka) and their modifications. Advanced algorithms: Fredman-Tarjan, Gabow et al. Randomized algorithms: Karger-Klein-Tarjan. Arborescenses of directed graphs, Edmond's branching algorithm.
- Flows in Networks. Revision - Ford-Fulkerson. Edmonds-Karp, Dinic's algorithm (and its variants), MPM (three Indians) algorithm. Modifications for restricted networks.
- Minimum Cuts in Undirected Graphs. All pairs flows/cuts: Gomory-Hu trees. Global minimum cut: node identification algorithm (Nagamochi-Ibaraki), random algorithms (Karger, Karger-Stein)
- Matchings in General Graphs. Basic algorithm using augmenting paths. Perfect matchings: Edmond's blossom algorithm. Maximum matchings.
- Graph Isomorphism. Colour refinement. Individualisation-refinement algorithms. Tractable classes of graphs.
- Dynamic Algorithms for Hard Problems. Dynamic programming on trees and circular-arc graphs. Tree-width; dynamic programming on tree-decompositions.
- Branching and Kernelization Algorithms for Hard Problems. Bounded search trees. Kernelization.

**Literature****Teaching methods**- Lecture 2 hrs/week plus 2hr tutorial each other week.
**Assessment methods**- Written exam. To obtain A or B students also have to pass the second, oral part of the exam.
**Language of instruction**- English
**Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (Autumn 2019, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2019/MA015