MA015 Graph Algorithms

Faculty of Informatics
Autumn 2006
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
RNDr. Václav Brožek, Ph.D. (seminar tutor)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc.
Timetable
Mon 14:00–15:50 A107
  • Timetable of Seminar Groups:
MA015/01: Mon 16:00–16:50 B011, L. Polák
MA015/02: Thu 9:00–9:50 B410, V. Brožek
Prerequisites
M005 Foundations of mathematics || MB005 Foundations of mathematics ||( MB101 Mathematics I && MB102 Mathematics II )
Ability of communication about basic mathematical objects and algorithms.
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
Course objectives
Basic graph algorithms are presented: searches, algorithms for minimal spanning trees, various algorithms for shortest paths and flows in nets.In all cases we prove the correctness and estimate the complexity.
Syllabus
  • Elementary graph algorithms (representations of graphs, breadth-first search, depth-first search, topological sort, strongly connected components).
  • Minimum spanning trees (growing a minimum spanning tree, the algorithms of Kruskal and Prim).
  • Single-source shortest paths (shortest paths and relaxation, Dijkstra's algorithm, the Bellman--Ford algorithm, single--source shortest paths in directed acyclic graphs).
  • All-pairs shortest paths (shortest paths and matrix multiplication, the Floyd-Warshall algorithm, Johnson's algorithm for sparse graphs).
  • Maximum flow (flow networks, the Ford-Fulkerson method, maximum bipartite matching).
  • Data structures for graph algorithms (binary heaps, priority queues, data structures for disjoint sets).
Literature
  • CORMEN, Thomas H., Charles Eric LEISERSON and Ronald L. RIVEST. Introduction to algorithms. Cambridge: MIT Press, 1990, xi, 1028. ISBN 0262031418. info
Assessment methods (in Czech)
Standardní přednáška. Ve cvičení studenti referují řešení předem zadaných úloh. Zkouška je písemná.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak/grafy.html
The course is also listed under the following terms Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, 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, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2006, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2006/MA015