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Algoritmični pristopi k problemu maksimalnega prereza grafov : magistrsko deloSmogavec, KsenijaProblem maksimalnega prereza grafa je najti takšno razbitje množice vozlišč grafa, da bo vsota uteži na povezavah, ki povezujejo ta dva kosa razbitja, največja. Problem maksimalnega prereza je ... NP-poln in je eden izmed osnovnih 21-ih Karpovih problemov. Zaradi njegove teoretične in praktične pomembnosti, aplikacije ima v statistični fiziki in vezjih, je bilo zapisanih že kar nekaj različnih aproksimacijskih algoritmov, hevristik ali kombinacij optimizacijskih metod in hevristik, ki rešujejo problem maksimalnega prereza. V magistrskem delu predstavimo problem maksimalnega prereza na posebnih razredih grafov, na katerih lahko najdemo rešitev problema v polinomskem času. Tretje poglavje je namenjeno Goemans Williamsonovemu aproksimacijskemu algoritmu, ki s pomočjo semidefinitnega programa najde rešitev, katere garantirana vrednost je vsaj 87 % optimalne rešitve in predstavlja prelom na področju aproksimacijskih algoritmiov. Poleg njunega algoritma predstavimo še Biq Mac algoritem, ki doseže skoraj optimalne rešitve za grafe z n % 100, in dualno skaliran algoritem, ki je primeren tudi za velike redke grafe. Temu sledi predstavitev posplošitve Goemans Williamsonovega algoritma za maksimalen k-prerez. Nazadnje predstavimo še nekaj hevristik, ki so učinkovite pri iskanju maksimalnega prereza.Type of material - master's thesis ; adult, seriousPublication and manufacture - Maribor : [K. Smogavec], 2014Language - slovenianCOBISS.SI-ID - 20542216
Author
Smogavec, Ksenija
Other authors
Bokal, Drago, 1978-
Topics
Matematika |
Teorija grafov |
Magistrska dela |
maksimalni prerez grafa |
semidefinitno programiranje |
hevristika |
NP-polni problemi |
graph theory |
max cut |
semidefinite programming |
heuristics |
NP-complete problem |
thesis
Call number – location, accession no. ... |
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Skladišče II 0000085885 Skladišče II 85885 |
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Smogavec, Ksenija | |
Bokal, Drago, 1978- | 22402 |
Source: Personal bibliographies
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