Course detail

Graph Algorithms

FIT-GALAcad. year: 2022/2023

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.

Language of instruction

Czech

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 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.

Course curriculum

Not applicable.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Text přednášek v elektronické podobě. (CS)
T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, MIT Press, 3. vydání, 1312 s., 2009. (CS)
T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, 3rd edition. MIT Press, 2009. (EN)
J. Demel, Grafy a jejich aplikace, Academia, 2002. (Více o knize) (CS)
J.A. McHugh, Algorithmic Graph Theory, Prentice-Hall, 1990.
K. Erciyes: Guide to Graph Algorithms (Sequential, Parallel and Discributed). Springer, 2018.

A. Mitina: Applied Combinatorics with Graph Theory. NEIU, 2019.


eLearning

eLearning: currently opened course

Classification of course in study plans

  • Programme IT-MGR-2 Master's

    branch MBI , any year of study, winter semester, elective
    branch MPV , any year of study, winter semester, elective
    branch MGM , any year of study, winter semester, elective
    branch MIS , any year of study, winter semester, elective
    branch MBS , any year of study, winter semester, elective
    branch MIN , any year of study, winter semester, elective
    branch MMM , any year of study, winter semester, compulsory

  • Programme MITAI Master's

    specialization NADE , any year of study, winter semester, elective
    specialization NBIO , any year of study, winter semester, elective
    specialization NGRI , any year of study, winter semester, elective
    specialization NNET , any year of study, winter semester, compulsory
    specialization NVIZ , any year of study, winter semester, elective
    specialization NCPS , any year of study, winter semester, elective
    specialization NSEC , any year of study, winter semester, elective
    specialization NEMB , any year of study, winter semester, elective
    specialization NEMB do 2021/22 , any year of study, winter semester, elective
    specialization NHPC , any year of study, winter semester, elective
    specialization NISD , any year of study, winter semester, elective
    specialization NIDE , any year of study, winter semester, elective
    specialization NISY do 2020/21 , any year of study, winter semester, elective
    specialization NISY , any year of study, winter semester, elective
    specialization NMAL , any year of study, winter semester, elective
    specialization NMAT , any year of study, winter semester, compulsory
    specialization NSEN , any year of study, winter semester, elective
    specialization NVER , any year of study, winter semester, elective
    specialization NSPE , any year of study, winter semester, elective

  • Programme IT-MGR-2 Master's

    branch MSK , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hours, 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, the Bellman-Ford algorithm, shortest path in DAGs.
  8. Dijkstra's algorithm. All-pairs shortest paths.
  9. Shortest paths and matrix multiplication, the Floyd-Warshall algorithm.
  10. Flows and cuts in networks, maximal flow, minimal cut, the Ford-Fulkerson algorithm.
  11. Matching in bipartite graphs, maximal matching.
  12. Graph coloring, Chromatic polynomial.
  13. Eulerian graphs and tours, Chinese postman problem, and Hamiltonian cycles.

Project

13 hours, compulsory

Teacher / Lecturer

Ing. Zbyněk Křivka, Ph.D.

Syllabus

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

eLearning

eLearning: currently opened course