Paralelni razveji in omeji algoritem BiqMac Solver

magistrsko delo

Alen Vegi Kalamar (Author), Drago Bokal (Mentor), Janez Povh (Co-mentor)

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

magistrska dela;maksimalen prerez grafa;semidefinitno programiranje;hevristike;algoritem razveji in omeji;paralelno računanje;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[A. Vegi Kalamar]
UDC:	519.178:004.421(043.2)
COBISS:	24058120
Views:	1001
Downloads:	133
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Parallel branch and bound BiqMac solver algorithm
Secondary 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.
Secondary keywords:	master theses;max cut;semidefinite programming;heuristics;branch and bound algorithm;parallel computation;
URN:	URN:SI:UM:
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	118 str.
ID:	10957869