# Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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Advanced Mathematics for Informatics - System Optimisation

A tantárgy neve magyarul / Name of the subject in Hungarian: Felsőbb matematika informatikusoknak - Rendszeroptimalizálás

Last updated: 2016. január 14.

 Budapest University of Technology and Economics Faculty of Electrical Engineering and Informatics MSc degree program in Software Engineering
 Course ID Semester Assessment Credit Tantárgyfélév VISZMA02 1 4/0/0/v 4
3. Course coordinator and department Dr. Szeszlér Dávid, Számítástudományi és Információelméleti Tanszék
Web page of the course http://cs.bme.hu/rendszeropt
4. Instructors

Dr. András Recski, professor, Department of Computer Science and Information Theory

Dr. Dávid Szeszlér, associate professor, Department of Computer Science and Information Theory

Dr. Gábor Wiener, associate professor, Department of Computer Science and Information Theory

6. Pre-requisites
Kötelező:
NEM ( TárgyEredmény( "BMEVISZM117" , "jegy" , _ ) >= 2
VAGY
TárgyEredmény("BMEVISZM117", "FELVETEL", AktualisFelev()) > 0)

A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

A kötelező előtanulmányi rendek grafikus formában itt láthatók.

7. Objectives, learning outcomes and obtained knowledge

The subject introduces some areas of operations research and combinatorial optimization. Besides covering the most relevant algorithms and methods and their limits, it also aims at giving a glimpse into some of their engineering applications. Thus the subject also covers some general algorithmic approaches like linear and integer programming and matroid theory. Furthermore, the course aims at extending and deepening the knowledge formerly provided by the Introduction to the Theory of Computing 1 and 2 and the Theory of Algorithms subjects of the BSc degree program in Software Engineering.

8. Synopsis Linear programming. Methods of solution, Farkas' lemma,
duality, integer programming, branch and bound, totally unimodular
matrices.
Matroid theory. Basic notions, greedy algorithm, duality, minors,
direct sum, algorithms, Tutte's and Seymour's theorems, rank function,
matroid matching.
Approximation algorithms. Additive and relative error, examples.
Scheduling algorithms. Types, algorithms of Hu, Coffman and Graham.
Reliable network design. Local edge connectivity, edge connectivity
number, algorithms of Nagamochi and Ibaraki, Karger, Khuller and
Vishkin, Cheriyan and Thurimella, Plesnik.
Applications in electrical networks and statics. Kichhoff's theorems,
rigidity of frameworks.
9. Method of instruction 4 hours of lecture per week
10. Assessment

Signature:

1 midterm during the semester the result of which has to be at least 40%.

Final:

Oral exam.

11. Recaps 2 occasions for retaking the midterm will be provided (the second one in the week preceding the exam period).
12. Consultations Subject to individual arrangements.
13. References, textbooks and resources Foulds, L. R. (2012). Combinatorial optimization for undergraduates. Springer Science & Business Media.
14. Required learning hours and assignment
 In class 56 Preparation for classes 12 Preparation for midterms 12 Homework Reading assignment Preparation for final 40 Total 120
15. Syllabus prepared by Dr. Dávid Szeszlér, associate professor, Department of Computer Science and Information Theory