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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

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

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

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

Martinjak, I. (2007). 'Konstrukcije dvoravnina pomoću kombinatoričkih algoritama', Scientific master's theses, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 25 April 2024, https://urn.nsk.hr/urn:nbn:hr:168:319837

Martinjak I. Konstrukcije dvoravnina pomoću kombinatoričkih algoritama [Scientific master's theses]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2007 [cited 2024 April 25] Available at: https://urn.nsk.hr/urn:nbn:hr:168:319837

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

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Metadata
TitleKonstrukcije dvoravnina pomoću kombinatoričkih algoritama
Title (english)Biplane constructions by means of combinatorial algorithms
AuthorIvica Martinjak
MentorMario-Osvin Pavčević (mentor)
Committee memberMarin Golub (predsjednik povjerenstva)
Committee memberMario-Osvin Pavčević (član povjerenstva)
Committee memberJuraj Šiftar (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
(Department of Applied Mathematics)
Zagreb
Defense date and country2007-01-09, 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)
Languagecroatian
URN:NBNurn:nbn:hr:168:319837
Promotion2007
Study programmeTitle: Postgraduate master programe in computing
Study programme type: university
Study level: postgraduate
Academic / professional title: magistar inženjer računarstva (magistar inženjer računarstva)
Type of resourceText
File originBorn digital
Access conditionsClosed access
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Created on2020-01-14 12:41:29

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