Graph Algorithms (in English)
GALe Acad. year 2022/2023 Winter semester 5 credits
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
- 39 hrs lectures
- 13 hrs projects
- 60 pts final exam
- 15 pts mid-term test
- 25 pts projects
Course Web Pages
Subject specific learning outcomes and competences
Fundamental ability to construct an algorithm for a graph problem and to analyze its time and space complexity.
Introduction to graph theory with focus on graph representations, graph algorithms and their complexities.
Prerequisite knowledge and skills
Foundations in discrete mathematics and algorithmic thinking.
- Electronic copy of lectures.
- T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, 3rd edition. MIT Press, 2009.
- J.A. McHugh, Algorithmic Graph Theory, Prentice-Hall, 1990.
- K. Erciyes: Guide to Graph Algorithms (Sequential, Parallel and Distributed). Springer, 2018.
A. Mitina: Applied Combinatorics with Graph Theory. NEIU, 2019.
Syllabus of lectures
- 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, Bellman-Ford algorithm, shortest path in DAGs.
- Dijkstra algorithm. All-pairs shortest paths.
- Shortest paths and matrix multiplication, Floyd-Warshall algorithm.
- Flows and cuts in networks, maximal flow, minimal cut, Ford-Fulkerson algorithm.
- Matching in bipartite graphs, maximal matching.
- Graph coloring.
- Eulerian graphs and tours, Hamiltonian graphs and cycles.
Syllabus - others, projects and individual work of students
- Solving of selected graph problems and presentation of solutions (principle, complexity, implementation, optimization).
- 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.
|Wed||exam||2022-11-09||C229||14:00||16:00||GALe: Midterm test|
|Wed||lecture||2022-09-21||M104 M105||14:00||16:50||9999||1EIT 2EIT INTE||xx|
|Wed||exam||2022-12-14||C229||15:00||17:30||GALe: Early exam|
Course inclusion in study plans
- Programme IT-MGR-2 (in English), field MGMe, any year of study, Elective
- Programme MIT-EN (in English), any year of study, Compulsory-Elective group B