Degree-Based Clique Relaxations

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Material Information

Title:
Degree-Based Clique Relaxations Theoretical Bounds, Computational Issues, and Applications
Physical Description:
1 online resource (187 p.)
Language:
english
Creator:
Shirokikh, Oleg A
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Industrial and Systems Engineering
Committee Chair:
BOGINSKIY,VLADIMIR L
Committee Co-Chair:
URYASEV,STANISLAV
Committee Members:
PARDALOS,PANAGOTE M
HAGER,WILLIAM WARD

Subjects

Subjects / Keywords:
clique-relaxations -- data-mining -- maximum-clique -- maximum-s-defective-clique -- maximum-s-plex -- optimization
Industrial and Systems Engineering -- Dissertations, Academic -- UF
Genre:
Industrial and Systems Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
This dissertation considers degree-based clique relaxations and their applications in real-world settings. A significant part of the study is devoted to two clique relaxation models, s-plex and s-defective clique, that have applications in social network analysis, bioinformatics and other areas.We investigate theoretical properties of these clique relaxations and provide analytical and computational bounds for the maximum s-plex and maximum s-defective clique problems. In addition, we obtain exact solutions for these problems and show their polynomial solvability for certain special classes of graphs. We propose new scale reduction techniques and attempt to find optimal solutions for both problems on extremely large sparse real-world networks. To our knowledge, this is the first comprehensive study of analytical and computational properties of these clique relaxations and the first attempt to solve the maximum s-plex and s-defective clique problems for very large network instances. Furthermore, using degree-based clique relaxations, we develop network-based data mining approaches to studying global characteristics of the U.S. stock market by utilizing several versions of the model referred to as the market graph. The graph instances were constructed using the following similarity measures reflecting the relationships between stocks: Pearson correlation, Spearman correlation, and Granger causality. The proposed techniques provide new approaches to revealing cohesive clusters of stocks, identifying profitable diversified portfolios and determining the most “influential” market entities. We show that the proposed approaches capture global properties of the stock market and its dynamics, as well as allow for a novel procedure of constructing an index that accurately reflects the trends of the entire market.The presented techniques are verified by computational experiments on historical data over the past decade.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Oleg A Shirokikh.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: BOGINSKIY,VLADIMIR L.
Local:
Co-adviser: URYASEV,STANISLAV.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-12-31

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0046078:00001