Faculty of Information Technology, BUT

Course details

Graph Algorithms

GAL Acad. year 2009/2010 Winter semester 5 credits

This course discusses graph representations and graphs algorithms for searching (depth-first search, breadth-first search), topological sorting, graph components and strongly connected components, minimal spanning trees, single-source and all-pairs shortest paths, maximal flows and minimal cuts, maximal bipartite matching, Euler graphs, and graph coloring. The basic principles and complexities of all presented algorithms are discussed.

Guarantor

Language of instruction

Czech

Completion

Examination (written+oral)

Time span

39 hrs lectures, 13 hrs projects

Assessment points

60 exam, 40 projects

Department

Lecturer

Instructor

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 kwnowledge and skills

Algorithmic thinking.

Study literature

  • Copy of lectures.
  • 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. (More about the book.)
  • 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 reprezentations.
  2. Graph searching, depth-first search, breadth-first search.
  3. Topological sort, acyklic 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.

Syllabus - others, projects and individual work of students

  1. Presentation of solutions of given assignments.

Progress assessment

  • Presentation of solutions of the given tasks (evaluated, max. 40 points, a part of the exam).
  • Final test (max. 60 points).

Controlled instruction

  • 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

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