## MA015 Graph Algorithms

Faculty of Informatics
Autumn 2023
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).
Taught in person.
Teacher(s)
doc. Mgr. Jan Obdržálek, PhD. (lecturer)
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 16:00–17:50 A218
• Timetable of Seminar Groups:
MA015/01: Mon 18. 9. to Mon 11. 12. each even Monday 10:00–11:50 A319, J. Obdržálek
Prerequisites
IB002 Algorithms I ||( TYP_STUDIA ( N )&& FAKULTA ( FI ))
Knowledge of basic graph algorithms and datastructures. Specifically, students should already understand the following datastructures and algorithms: Graphs searching: DFS, BFS. Network flows: Ford-Fulkerson. Minimum spanning trees: at least one of Boruvka, Jarnik (Prim), Kruskal. Shortest paths: Bellman-Ford, Dijkstra. Datastructures: priority queues, 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 surveys important graph algorithms beyond those typically covered in basic algorithms and data structures courses. Chosen algorithms span most of the important application areas of graphs algorithms.
Learning outcomes
At the end of the course students will:
- know and understand efficient algorithms for various graph problems, including: minimum spanning trees, network flows, (globally) minimum cuts, matchings (including the assignment problem);
- be able to prove correctness and complexity of these algorithms;
- be able to use dynamic programming to solve problems on tree-like graphs;
- learn a range of techniques useful for designing efficient algorithms and deriving their 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. Min-cost perfect matching: Hungarian algorithm.
• Dynamic Algorithms for Hard Problems. Dynamic programming on trees and circular-arc graphs. Tree-width; dynamic programming on tree-decompositions.
• Graph Isomorphism. Colour refinement. Individualisation-refinement algorithms. Tractable classes of graphs.
Literature
recommended literature
• MAREŠ, Martin. Krajinou grafových algoritmů. Pracovní verze. ITI, 2015. URL info
• CORMEN, Thomas H., Charles Eric LEISERSON and Ronald L. RIVEST. Introduction to algorithms. Cambridge: MIT Press, 1990. xi, 1028. ISBN 0262031418. info
Teaching methods
Lecture 2 hrs/week plus tutorial every 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.
The course is also listed under the following terms Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022.
• Enrolment Statistics (recent)
• Permalink: https://is.muni.cz/course/fi/autumn2023/MA015