Course detail
Graph Algorithms
FIT-GALAcad. year: 2019/2020
This course discusses graph representations and graphs algorithms for searching (depth-first search, breadth-first search), topological sorting, graph components and strongly connected components, trees and minimal spanning trees, single-source and all-pairs shortest paths, maximal flows and minimal cuts, maximal bipartite matching, Euler graphs, and graph coloring. The principles and complexities of all presented algorithms are discussed.
Supervisor
Department
Learning outcomes of the course unit
Fundamental ability to construct an algorithm for a graph problem and to analyze its time and space complexity.
Prerequisites
Foundations in discrete mathematics and algorithmic thinking.
Co-requisites
Not applicable.
Recommended optional programme components
Not applicable.
Recommended or required reading
Text přednášek.
T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, MIT Press, 3. vydání, 1312 s., 2009.
T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms (http://www.introductiontoalgorithms.com), McGraw-Hill, 2002.
J. Demel, Grafy, SNTL Praha, 1988.
J. Demel, Grafy a jejich aplikace, Academia, 2002. (Více o knize (http://kix.fsv.cvut.cz/~demel/grafy/))
R. Diestel, Graph Theory, Third Edition (http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/), Springer-Verlag, Heidelberg, 2000.
J.A. McHugh, Algorithmic Graph Theory, Prentice-Hall, 1990.
J.A. Bondy, U.S.R. Murty: Graph Theory, Graduate text in mathematics, Springer, 2008.
J.L. Gross, J. Yellen: Graph Theory and Its Applications, Second Edition, Chapman & Hall/CRC, 2005.
J.L. Gross, J. Yellen: Handbook of Graph Theory (Discrete Mathematics and Its Applications), CRC Press, 2003.
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
- Mid-term written examination (15 point)
- Evaluated project(s) (25 points)
- Final written examination (60 points)
- The
minimal number of points which can be obtained from the final exam is
25. Otherwise, no points will be assigned to a student.
Language of instruction
Czech, English
Work placements
Not applicable.
Aims
Familiarity with graphs and graph algorithms with their complexities.
Specification of controlled education, way of implementation and compensation for absences
In case of illness or another serious obstacle, the student should
inform the faculty about that and subsequently provide the evidence of
such an obstacle. Then, it can be taken into account within evaluation:
- The student can ask the responsible teacher to extend the time for the project assignment.
- If a student cannot attend the mid-term exam, (s)he can ask to derive points from the evaluation of his/her first attempt of the final exam.
Classification of course in study plans
- Programme IT-MGR-2 Master's
branch MBI , any year of study, winter semester, 5 credits, optional
branch MPV , any year of study, winter semester, 5 credits, optional
branch MGM , any year of study, winter semester, 5 credits, optional
branch MIS , any year of study, winter semester, 5 credits, optional
branch MBS , any year of study, winter semester, 5 credits, optional
branch MIN , any year of study, winter semester, 5 credits, optional
branch MMI , any year of study, winter semester, 5 credits, optional
branch MMM , any year of study, winter semester, 5 credits, compulsory - Programme MITAI Master's
specialization NADE , any year of study, winter semester, 5 credits, optional
specialization NBIO , any year of study, winter semester, 5 credits, optional
specialization NGRI , any year of study, winter semester, 5 credits, optional
specialization NNET , any year of study, winter semester, 5 credits, compulsory
specialization NVIZ , any year of study, winter semester, 5 credits, optional
specialization NCPS , any year of study, winter semester, 5 credits, optional
specialization NSEC , any year of study, winter semester, 5 credits, optional
specialization NEMB , any year of study, winter semester, 5 credits, optional
specialization NHPC , any year of study, winter semester, 5 credits, optional
specialization NISD , any year of study, winter semester, 5 credits, optional
specialization NIDE , any year of study, winter semester, 5 credits, optional
specialization NISY , any year of study, winter semester, 5 credits, optional
specialization NMAL , any year of study, winter semester, 5 credits, optional
specialization NMAT , any year of study, winter semester, 5 credits, compulsory
specialization NSEN , any year of study, winter semester, 5 credits, optional
specialization NVER , any year of study, winter semester, 5 credits, optional
specialization NSPE , any year of study, winter semester, 5 credits, optional - Programme IT-MGR-2 Master's
branch MSK , 1. year of study, winter semester, 5 credits, compulsory
Type of course unit
Lecture
39 hours, optionally
Teacher / Lecturer
Syllabus
- Introduction, algorithmic complexity, basic notions and graph representations.
- Graph searching, depth-first search, breadth-first search.
- Topological sort, acyclic graphs.
- Graph components, strongly connected components, examples.
- Trees, minimal spanning trees, algorithms of Jarník and Borůvka.
- Growing a minimal spanning tree, algorithms of Kruskal and Prim.
- Single-source shortest paths, the Bellman-Ford algorithm, shortest path in DAGs.
- Dijkstra's algorithm. All-pairs shortest paths.
- Shortest paths and matrix multiplication, the Floyd-Warshall algorithm.
- Flows and cuts in networks, maximal flow, minimal cut, the Ford-Fulkerson algorithm.
- Matching in bipartite graphs, maximal matching.
- Graph coloring, Chromatic polynomial.
- Eulerian graphs and tours, Chinese postman problem, and Hamiltonian cycles.
Project
13 hours, compulsory
Teacher / Lecturer
Syllabus
- Solving of selected graph problems and presentation of solutions (principle, complexity, implementation, optimization).
eLearning
eLearning: currently opened course