MA015 Graph Algorithms

Faculty of Informatics
Autumn 2021
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)
Guaranteed by
doc. Mgr. Jan Obdržálek, PhD.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Mon 13. 9. to Mon 6. 12. Mon 12:00–13:50 A320
  • Timetable of Seminar Groups:
MA015/01: Tue 14. 9. to Tue 7. 12. each odd Tuesday 16:00–17:50 A320, 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 and datastructures. Specifically, students should already understand the following datastructures and algorithms: Graphs searching: DFS, BFS. Network flows: Ford-Fulkerson. Minimum spanning trees: 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 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. 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 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2021, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2021/MA015