Improvements On Spectral Bisection
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00539510" target="_blank" >RIV/67985807:_____/20:00539510 - isvavai.cz</a>
Výsledek na webu
<a href="http://hdl.handle.net/11104/0317243" target="_blank" >http://hdl.handle.net/11104/0317243</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.13001/ela.2020.4993" target="_blank" >10.13001/ela.2020.4993</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Improvements On Spectral Bisection
Popis výsledku v původním jazyce
In this paper, the third eigenvalue of the Laplacian matrix is used to provide a lower bound on the minimum cutsize. This result has algorithmic implications that are exploited in this paper. Besides, combinatorial properties of certain configurations of a graph partition which are related to the minimality of a cut are investigated. It is shown that such configurations are related to the third eigenvector of the Laplacian matrix. It is well known that the second eigenvector encodes structural information, and that can be used to approximate a minimum bisection. In this paper, it is shown that the third eigenvector carries structural information as well. Then a new spectral bisection algorithm using both eigenvectors is provided. The new algorithm is guaranteed to return a cut that is smaller or equal to the one returned by the classic spectral bisection. Also, a spectral algorithm that can refine a given partition and produce a smaller cut is provided.
Název v anglickém jazyce
Improvements On Spectral Bisection
Popis výsledku anglicky
In this paper, the third eigenvalue of the Laplacian matrix is used to provide a lower bound on the minimum cutsize. This result has algorithmic implications that are exploited in this paper. Besides, combinatorial properties of certain configurations of a graph partition which are related to the minimality of a cut are investigated. It is shown that such configurations are related to the third eigenvector of the Laplacian matrix. It is well known that the second eigenvector encodes structural information, and that can be used to approximate a minimum bisection. In this paper, it is shown that the third eigenvector carries structural information as well. Then a new spectral bisection algorithm using both eigenvectors is provided. The new algorithm is guaranteed to return a cut that is smaller or equal to the one returned by the classic spectral bisection. Also, a spectral algorithm that can refine a given partition and produce a smaller cut is provided.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
<a href="/cs/project/GJ16-07822Y" target="_blank" >GJ16-07822Y: Extremální teorie grafů a aplikace</a><br>
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Electronic Journal of Linear Algebra
ISSN
1081-3810
e-ISSN
—
Svazek periodika
36
Číslo periodika v rámci svazku
December
Stát vydavatele periodika
IL - Stát Izrael
Počet stran výsledku
21
Strana od-do
857-877
Kód UT WoS článku
000608278800001
EID výsledku v databázi Scopus
—