Problem traženja Ramseyevih brojeva

undergraduate thesis

• Title (english): Problem of Finding Ramsey Numbers
• Author: Hrvoje Bušić
• Mentor: Tomislav Burić (mentor)
• Committee member: Tomislav Burić (predsjednik povjerenstva)
• Committee member: Anamari Nakić (član povjerenstva)
• Committee member: Ana Anušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2017-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Ramseyeva teorija za danu strukturu za koju se vjeruje da posjeduje određeno svojstvo, želi odrediti uvjete pod kojima će struktura ostvariti upravo promatrano svojstvo.
Matematičari i računalni znanstvenici iz raznih smjerova i na različite načine pokušavaju pristupiti jezgrenom problemu Ramseyevog teorema: eksponencijalno rastućem prostoru pretraživanja stanja u obliku bojanih grafova.
Naivni pristup iscrpnog pretraživanja prostora stanja se pokazao neodgovarajućim čak i za male Ramseyeve brojeve, čime pokušaji rješavanja teorema privlače brojne implementacije naprednih algoritama i metaheuristika.
Metaheuristike se nadalje osnažuju znanjem iz domene problema, stečenim kroz iskustvo istraživača koji se godinama bave teoremom.

Abstract (english)

Ramsey's theory for a given structure believed to possess a certain property wants to determine the conditions under which the structure will realize the just observed property.
Mathematicians and computer scientists from different directions and in various ways try to approach the core problem of Ramsey's theorem: an exponentially growing search space in the form of painted graphs.
The brute force approach has proved inadequate even for small Ramsey numbers, which led to attempts to solve the theorem with implementations of advanced algorithms and metaheuristics.
Metaheuristics are continuously improved with knowledge of the problem domain, gained through the experience of researchers who have been dealing with the theorem for years.

• Keywords: graf; klika; Bron-Kerbosch algoritam traženja klika; Frank P. Ramsey; Ramseyeva teorija; Ramseyev teorem; Ramseyevi brojevi
• Keywords (english): graph; clique; Bron-Kerbosch clique finding algorithm; Frank P. Ramsey; Ramsey theory; Ramsey theorem; Ramsey numbers
• Language: croatian
• URN:NBN: urn:nbn:hr:168:249570
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-13 19:29:59