Algorithm complexity

Description of algorithm time and space complexity, methods of expressing it, effective comparison of algorithms by means of such metrics, examples of complexity in basic graph operations.

Advanced programming methods

Description of advanced programming methods, such as recursion or dynamic programming, their use for graph search.

Advanced sort and search methods

Description of advanced sort and search methods (e.g. merge sort, quicksort, BB(a) tree, B-tree, Boyer-Moore algorithm text search etc.).

Standard data algorithms

Description of various standard algorithm methods for ordering and search, including relevant features of algorithms, lowering the complexity of handling graphs by means of more effective data administration methods.

Heuristic problem solving

Hungry algorithms and implementing heuristics, introduction of the simplicity of hungry algorithms via the minimal graph frame.

Complexity classes

Introducing complexity classes P and NP, the differences and potential relation, NP-full problems, demonstrating the issue of colour as an NP-full problem.

Approximation and vague algorithms

Introducing the topic of vague and approximation algorithms, methods of solving the issue of colour via polynomial algorithms.

Graph and its storage in a computer

Representing real problems by means of a graph and its effective storage in a computer with regard to the solved problem, oriented graphs, the use of general algorithm complexity definitions.

Graph passage

Basic methods of passing through a graph in depth and width, their use for graph characterisation and real task implementation, the use of search for the shortest path algorithm. The use of advanced algorithm methods, such as recursion or dynamic programming.

Trees

Characteristics of trees, their coding and thereby enabled effective storage in memory, the related problem of tree isomorphism.

The issue of minimal frame

Finding the frame and its minimisation, the complexity of the whole approach and the simple hungry algorithm for solutions, the use of the knowledge of general heuristic methods.

The issue of colour

The issue of graph colour, the use for planning algorithms, the complexity of the problem and its NP-fullness, the relation to the general definition of complexity classes.

Vague algorithms in graph colour

Algorithms for approximate graph colouring, approaches to solving complex algorithms polynomially with a certain degree of inaccuracy, related to the general definition of approximation and vague algorithms.