Kombinatoricka a vypocetni geometrie I 2017/2018

Combinatorial and Computational Geometry I 2017/2018

(Jan Kyncl, Pavel Valtr, KAM)

Prednaska: v utery od 14:00 v S3.
Lecture: Tuesdays at 14:00 in S3.

Cviceni: po prednasce 15:40 v S3 podle rozvrhu na strance cviceni.
Exercise sessions: after the lecture at 15:40 in S3 according to the schedule on the exercise webpage.


Rozsah vyuky: ZIMNI semestr 2/2 Z, Zk. Záznam v SISu, sylabus
Extent of teaching: WINTER semester 2/2 (Exam and Exercise credit). Entry in SIS, syllabus

Anotace
Vypocetni geometrie se zabyva navrhem efektivnich algoritmu pro geometricke problemy v rovine i ve vicedimenzionalnim prostoru (napr. je-li dano n bodu v rovine, jak co nejefektivneji najit dvojici bodu s nejmensi vzdalenosti). Takove problemy jsou motivovany aplikacemi v pocitacove grafice, prostorovem modelovani (napr. molekul, budov, soucastek), geografickych informacnich systemech a pod. Pri analyze takovych algoritmu se potrebuje kombinatoricka geometrie, studujici kombinatoricke vlastnosti geometrickych konfiguraci, konvexnich mnozin a pod. Vysledky jsou dulezite i z ciste matematickeho hlediska, napr. v teorii cisel. V teto uvodni prednasce se probiraji zakladni pojmy a metody, s durazem na matematicky zaklad (jine mozne podani by bylo z vice "informatickeho" hlediska, s durazem na datove struktury, implementaci algoritmu apod.). O naplni prednasky si muzete udelat lepsi predstavu podle latky probirane v minulych letech.

Annotation
Discrete geometry investigates combinatorial properties of geometric objects such as finite point sets or convex sets in Euclidean spaces. Computational geometry considers the design of efficient algorithms for computing with geometric configurations, and discrete geometry serves as its mathematical foundation. Part I of the course is a concise introduction. The lecture will be very similar to the last year. The contents of Part II varies among the years, each year covering a few selected topics in more depth.

Literatura

Literature

Temata prednasek:

3.10. (JK)

10.10. (JK)

17.10. (JK)

...

5.12. (PV, JK)

12.12. (JK)

Topics covered:

3.10. (JK)

10.10. (JK)

17.10. (JK)

...

5.12. (PV, JK)

12.12. (JK)