Paralelni razveji in omeji algoritem BiqMac Solver

Vegi Kalamar, Alen

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Title:	Paralelni razveji in omeji algoritem BiqMac Solver
Authors:	ID Vegi Kalamar, Alen (Author) ID Bokal, Drago (Mentor) More about this mentor... ID Povh, Janez (Comentor)
Files:	MAG_Vegi_Kalamar_Alen_2018.pdf (908,74 KB) MD5: 338C602AD68962F3C0520255B5BECE72 PID: 20.500.12556/dkum/4451034a-5bb3-4108-b601-98cac3e1fa96
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	Problem maksimalnega prereza je primer NP težkega problema. To pomeni, da ne poznamo učinkovitega polinomskega algoritma za reševanje problema za poljuben graf in domnevamo, da tudi ne obstaja. Kljub temu obstajajo pristopi, kako reševati problem do optimalnosti. V kolikor poznamo učinkovite hevristike in poenostavitve problema, je primeren pristop algoritem razveji in omeji. Rendl, Rinaldi in Wiegele so z uporabo različnih poenostavitev, dualne teorije, aproksimacijskih algoritmov in hevristik razvili učinkovit algoritem razveji in omeji z imenom BiqMac Solver, ki optimalno reši problem maksimalnega prereza tudi za večje grafe. Zaradi strukture je algoritem primeren, da ga implementiramo za paralelno izvajanje. Namen magistrskega dela je predstavitev algoritma BiqMac in njegova paralelna implementacija.
Keywords:	maksimalen prerez grafa, semidefinitno programiranje, hevristike, algoritem razveji in omeji, paralelno računanje
Place of publishing:	Maribor
Publisher:	[A. V. Kalamar]
Year of publishing:	2018
PID:	20.500.12556/DKUM-72022
UDC:	519.178:004.421(043.2)
COBISS.SI-ID:	24058120
NUK URN:	URN:SI:UM:DK:AU08UJQE
Publication date in DKUM:	04.10.2018
Views:	2092
Downloads:	252
Metadata:
Categories:	FNM
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Licences

License:	CC BY-SA 4.0, Creative Commons Attribution-ShareAlike 4.0 International

Link:	http://creativecommons.org/licenses/by-sa/4.0/
Description:	This Creative Commons license is very similar to the regular Attribution license, but requires the release of all derivative works under this same license.
Licensing start date:	06.09.2018

Secondary language

Language:	English
Title:	Parallel branch and bound BiqMac Solver Algorithm
Abstract:	The max cut problem is a NP hard problem. That means that no effective algorithm for this problem is known, and it is conjectured that none exists. However, there are a few possible methods of optimally solving these problems. If the efficient heuristics and relaxations of the problem are known, a correct procedure is using a branch and bound algorithm. Using various relaxations, duality theory, approximation algorithms and heuristics, Rendl, Rinaldi and Wiegele developed an effective branch and bound algorithm called BiqMac Solver, which optimally solves max cut problems, even for large graphs. Because of its structure, the algorithm is appropriate for parallel computing. The purpose of this master’s thesis is to present the BiqMac algorithm and its parallel implementation.
Keywords:	max cut, semidefinite programming, heuristics, branch and bound algorithm, parallel computation

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