Combinatorial Algorithms

The course is not on the list Without time-table
Code Completion Credits Range Language
RM35KOA Z,ZK 6 2P+2C Czech
Garant předmětu:
Department of Control Engineering

The goal is to show the problems and algorithms of combinatorial optimization (often called discrete optimization; there is a strong overlap with the term operations research).

Following the courses on linear algebra, graph theory, and basics of optimization, we show optimization techniques based on graphs, integer linear programming, heuristics, approximation algorithms and state space search methods.

We focus on application of optimization in stores, ground transportation, flight transportation, logistics, planning of human resources, scheduling in production lines, message routing, scheduling in parallel computers.


Optimisation, Discrete mathematics, Logics and graphs

Syllabus of lectures:

1. Introduction to Basic Terms of Combinatorial Optimization, Example Applications, and a Test of Preliminary Knowledge

2. Complexity of combinatorial problems

3. Integer Linear Programming - Algorithms

4. Problem Formulation by Integer Linear Programming

5. The Shortest Paths. Problem Formulation by Shortest Paths.

6. Problem Formulation by Shortest Paths. Test I.

7. Flows and Cuts - Algorithms.

8. Flows and Cuts - Problem Formulation.

9. Multicommodity network flows.

10. Knapsack Problem and Pseudo-polynomial Algorithms.

11. Traveling Salesman Problem and Approximation Algorithms.

12. Monoprocessor Scheduling.

13. Scheduling on Parallel Processors.

14. Reserved

Syllabus of tutorials:

1. Introduction to the Experimental Environment and Optimization Library

2. SAT and nteger Linear Programming

3. Integer Linear Programming

4. Integer Linear Programming

5. Individual Project I - Assignment and Problem Classification

6. Traveling Salesman Problem

7. Individual Project II - Related Work and Solution

8. Applications of Network Flows and Cuts

9. Individual Project III - Consultation

10. Scheduling. Test II

11. Advanced Methods for Solving Combinatorial Problems

12. Individual Project IV - evaluation and written report

13. Ungraded Assessment

14. Reserved

Study Objective:
Study materials:

B. H. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms.

Springer, sixth ed., 2018.


J. Blazevicz, Scheduling Computer and Manufacturing Processes. Springer,

second ed., 2001.

J. Demel, Grafy a jejich aplikace. Academia, second ed., 2015.


Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-06-12
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