Course details

Graph Algorithms

GAL Acad. year 2017/2018 Winter semester 5 credits

Current academic year

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.

Guarantor

Meduna Alexandr, prof. RNDr., CSc. (DIFS)

Language of instruction

Czech, English

Completion

Examination (written)

Time span

  • 39 hrs lectures
  • 13 hrs projects

Assessment points

  • 60 pts final exam (written part)
  • 15 pts mid-term test (written part)
  • 25 pts projects

Department

Department of Information Systems (UIFS)

Subject specific learning outcomes and competences

Fundamental ability to construct an algorithm for a graph problem and to analyze its time and space complexity.

Learning objectives

Familiarity with graphs and graph algorithms with their complexities.

Prerequisite knowledge and skills

Foundations in discrete mathematics and algorithmic thinking.

Study literature

  • Text přednášek.
  • T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, McGraw-Hill, 2002.

Fundamental literature

  • T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, McGraw-Hill, 2002.
  • J. Demel, Grafy, SNTL Praha, 1988.
  • J. Demel, Grafy a jejich aplikace, Academia, 2002. (Více o knize)
  • R. Diestel, Graph Theory, Third Edition, 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.

Syllabus of lectures

  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. Euler graphs and tours and Hamilton cycles.
  13. Graph coloring.

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

A written mid-term exam, an evaluation of projects, and a final exam. 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 inclusion in study plans

Back to top