Table of Contents

B4M35KO+BE4M35KO -- Combinatorial Optimization

Lecturer: Zdeněk Hanzálek

Lab teachers: Anna Minaeva, Theodor Krocan, István Módos, Antonín Novák and Marek Vlk

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Course overview

This course is focusing on the problems and algorithms of combinatorial optimization (often called discrete optimization). 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, e.g. logistics, transportation, planning of human resources, scheduling in production lines, message routing and scheduling in parallel computers.


Optimization, Discrete Mathematics, Logics and Graph Theory.


This timetable is for the czech version (B4M35KO) of the course. The timetable of the english version (BE4M35KO) is provided by prof. Hanzálek.

Week No. Title Notes Handouts
1 Introduction of Basic Terms, Example Applications Test 0
2 Integer Linear Programming - Algorithms
3 Integer Linear Programming - Problem Formulations
4 Shortest Paths
5 Problem Formulation by Shortest Paths
6 Flows and Cuts - Algorithms and Problem Formulation Test I.
7 Bipartite Matching. Multi-commodity Network Flows
8 Knapsack Problem, Pseudo-polynomial and Approximation Algorithms
9 Traveling Salesman Problem and Approximation Algorithms
10 Mono-processor Scheduling
11 lecture cancelled
12 lecture cancelled
13 Tuesday Scheduling on Parallel Processors Test II.
13 Thursday Project Scheduling with Time Windows
14 Constraint Programming


To get an ungraded assessment the following requirements have to be met:

To pass the exam it is necessary to get at least 20 points (maximum 40 points) from the written exam. The oral exam is mandatory and gives 10 points at maximum.

Final grading scale:

Points [0,50) [50,60) [60,70) [70,80) [80,90) [90,100]
Grade F E D C B A

Assessment recognition

The following applies only to students who got an ungraded assessment in the previous year (all other students have to undergo the course from scratch).

Although the assessments are not fully recognized, the students may opt-in to transfer some points from the previous year to the current one (they may also undergo the course from scratch to get a higher number of points). The following rules apply

  1. Tests I, II, practical test and the homeworks have to be repeated.
  2. Students may transfer points from the semester project. If the grading table of the course changes between the years, the points are scaled accordingly. It is also possible to work on the same topic to increase/decrease the number of received points.
  3. The minimum number of points required to get an ungraded assessment is always taken from the current year grading table.