Konstrukcije dvoravnina pomoću kombinatoričkih algoritama

Martinjak, Ivica

prikaz prve stranice dokumenta Konstrukcije dvoravnina pomoću kombinatoričkih algoritama

No public access

scientific master's theses

Konstrukcije dvoravnina pomoću kombinatoričkih algoritama

Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2007. urn:nbn:hr:168:319837

Martinjak, Ivica

University of Zagreb
Faculty of Electrical Engineering and Computing
Department of Applied Mathematics

Cite this document

APA 6th Edition

Martinjak, I. (2007). Konstrukcije dvoravnina pomoću kombinatoričkih algoritama (Scientific master's theses). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:319837

MLA 8th Edition

Martinjak, Ivica. "Konstrukcije dvoravnina pomoću kombinatoričkih algoritama." Scientific master's theses, University of Zagreb, Faculty of Electrical Engineering and Computing, 2007. https://urn.nsk.hr/urn:nbn:hr:168:319837

Chicago 17th Edition

Harvard

Martinjak, I. (2007). 'Konstrukcije dvoravnina pomoću kombinatoričkih algoritama', Scientific master's theses, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 21 September 2024, https://urn.nsk.hr/urn:nbn:hr:168:319837

Vancouver

Martinjak I. Konstrukcije dvoravnina pomoću kombinatoričkih algoritama [Scientific master's theses]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2007 [cited 2024 September 21] Available at: https://urn.nsk.hr/urn:nbn:hr:168:319837

IEEE

I. Martinjak, "Konstrukcije dvoravnina pomoću kombinatoričkih algoritama", Scientific master's theses, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2007. Available at: https://urn.nsk.hr/urn:nbn:hr:168:319837

Cite this item: https://urn.nsk.hr/urn:nbn:hr:168:319837

Please login to the repository to save this object to your list.

Metadata

Title	Konstrukcije dvoravnina pomoću kombinatoričkih algoritama
Title (english)	Biplane constructions by means of combinatorial algorithms
Author	Ivica Martinjak
Mentor	Mario-Osvin Pavčević (mentor)
Committee member	Marin Golub (predsjednik povjerenstva)
Committee member	Mario-Osvin Pavčević (član povjerenstva)
Committee member	Juraj Šiftar (član povjerenstva)
Granter	University of Zagreb Faculty of Electrical Engineering and Computing (Department of Applied Mathematics) Zagreb
Defense date and country	2007-01-09, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics Discrete and Combinatorial Mathematics
Universal decimal classification (UDC)	51 - Mathematics
Abstract	Dvoravnine su simetrični dizajni s parametrima 2 - (v, k,2) . Do sada je poznato sedamnaest dvoravnina, sa sedam različitih trojki parametara. Pri tome, dvoravnine s 56 i 79 točaka nisu klasificirane, već su poznati samo pojedini primjeri. Dvoravnine su strukture visoke pravilnosti čija veličina prostora rješenja izrazito raste s brojem točaka (kombinatorička eksplozija). Dodatna poteškoća pri konstrukciji ovih struktura je vrlo mali broj struktura (rezultata) u prostoru pretraživanja. Determinističkim algoritmom (iscrpnom pretragom) klasificirane su dvoravnine redova 2, 3, 4 i 7. Pretragom uz dodatno pretpostavljeni uvjet (jedinice na glavnoj dijagonali incidencijske matrice) konstruirane su dvije dvoravnine 2 - (56,11,2) . Prilikom pretrage uz taj uvjet, kod 2 - (37,9,2) uočena je jednoznačna odrenenost broja incidencijskih matrica brojem odgovarajućih vektora iz (k + 2) -og retka. Analogna se pravilnost javlja i na ispitanom uzorku 2 - (56,11,2) . U eksperimentima s heurističkim algoritmima, pokazalo se da konstrukcija pomoću Hussainovih grafova ima manji prostor rješenja nego konstrukcija pomoću matrica incidencije, uz odrenene pretpostavke. Najveći utjecaj na doseg imalo je matematičko pojednostavljenje problema, postavljanje dodatnog uvjeta na strukturu te filtriranje vektora.
Abstract (english)	A biplane is a symmetric 2 − (v, k,2) design. Until now, seventeen biplanes with seven different triple of parameters are known. Out of which, biplanes with 56 and 79 points are not classified but only a few individual examples are known. Biplanes are highly regular structures, the space solution size of which extremely increases with number of points (combinatorial explosion). Additional difficulty in construction of this structure is a very small number of structures (results) in space solution. Biplanes of order 2, 3, 4 and 7 are classified by deterministic algorithm (exhaustive search). By searching using additional presumptive condition (each element on the main diagonal of incidence matrix is 1) two biplanes 2 − (56,11,2) are constructed. By searching using the same condition in the case of 2 − (37,9,2) it is observed that a number of incidence matrix is unambiguously determined by number of appropriate vectors of (k + 2) nd row. An analogous regularity appears on testing sample 2 − (56,11,2) . Experiments with heuristic algorithms showed that construction according to Hussain graphs has smaller space solution than construction with incidence matrix, on certain assumptions. Mathematical simplification of problem, using additional condition on structure and vector filtering had the main impact on achievement.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:168:319837
Promotion	2007
Study programme	Title: Postgraduate master programe in computing Study programme type: university Study level: postgraduate Academic / professional title: magistar inženjer računarstva (magistar inženjer računarstva)
Type of resource	Text
File origin	Born digital
Access conditions	Closed access
Terms of use
Repository	FER Repository
Created on	2020-01-14 12:41:29