Improvements On Spectral Bisection
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Improvements On Spectral Bisection
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ16-07822Y" target="_blank" >GJ16-07822Y: Extremal graph theory and applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Linear Algebra
ISSN
1081-3810
e-ISSN
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Volume of the periodical
36
Issue of the periodical within the volume
December
Country of publishing house
IL - THE STATE OF ISRAEL
Number of pages
21
Pages from-to
857-877
UT code for WoS article
000608278800001
EID of the result in the Scopus database
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