Course detail

Graph Algorithms (in English)

FIT-GALeAcad. year: 2022/2023

This course discusses graph representations and graphs algorithms for searching (depth-first search, breadth-first search), topological sorting, searching of 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.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. RNDr. Alexandr Meduna, CSc.

Department

Department of Information Systems (UIFS)

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.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

  • Mid-term exam - 15 points.
  • Projects - 25 points.
  • Final exam - 60 points. The minimal number of points which can be obtained from the final exam is 25. Otherwise, no points from the final exam will be assigned to a student.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Introduction to graph theory with focus on graph representations, graph algorithms and their complexities.

Specification of controlled education, way of implementation and compensation for absences

 

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Electronic copy of lectures. (EN)
J. Demel, Grafy, SNTL Praha, 1988. (CS)
J. Demel, Grafy a jejich aplikace, Academia, 2002. (Více o knize) (CS)
J.A. McHugh, Algorithmic Graph Theory, Prentice-Hall, 1990. (EN)
K. Erciyes: Guide to Graph Algorithms (Sequential, Parallel and Distributed). Springer, 2018. (EN)
A. Mitina: Applied Combinatorics with Graph Theory. NEIU, 2019. (EN)
T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, 3rd edition. MIT Press, 2009. (EN)

Classification of course in study plans

  • Programme IT-MSC-2 Master's

    branch MGMe , 0 year of study, winter semester, elective

  • Programme MIT-EN Master's 0 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

Ing. Zbyněk Křivka, Ph.D.

Syllabus

  1. Introduction, algorithmic complexity, basic notions and graph representations.
  2. Graph searching, depth-first search, breadth-first search.
  3. Topological sort, acyclic graphs.
  4. Graph components, strongly connected components, examples.
  5. Trees, minimal spanning trees, algorithms of Jarník and Borůvka.
  6. Growing a minimal spanning tree, algorithms of Kruskal and Prim.
  7. Single-source shortest paths, Bellman-Ford algorithm, shortest path in DAGs.
  8. Dijkstra algorithm. All-pairs shortest paths.
  9. Shortest paths and matrix multiplication, Floyd-Warshall algorithm.
  10. Flows and cuts in networks, maximal flow, minimal cut, Ford-Fulkerson algorithm.
  11. Matching in bipartite graphs, maximal matching.
  12. Graph coloring.
  13. Eulerian graphs and tours, Hamiltonian graphs and cycles.

Project

13 hod., compulsory

Teacher / Lecturer

Ing. Zbyněk Křivka, Ph.D.

Syllabus

  1. Solving of selected graph problems and presentation of solutions (principle, complexity, implementation, optimization).