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New algorithmic and hardness results for graph partitioning problems
Descriptive
TitleInfo
Title
New algorithmic and hardness results for graph partitioning problems
Name
(type = personal)
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Kaminski
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Marcin Jakub
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Marcin Kaminski
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author
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Lozin
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Vadim
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Advisory Committee
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Vadim Lozin
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chair
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Saks
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Michael
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Michael Saks
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internal member
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Gurvich
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Vladimir
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Advisory Committee
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Vladimir Gurvich
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internal member
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Boros
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Endre
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Advisory Committee
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Endre Boros
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internal member
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Thilikos
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Dimitrios
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Advisory Committee
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Dimitrios Thilikos
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outside member
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Rutgers University
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degree grantor
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Graduate School-New Brunswick
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theses
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2007
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2007
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English
PhysicalDescription
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electronic
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iv, 63 pages
Abstract
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In this thesis we study algorithmic aspects of two graph partitioning problems -- graph coloring and maximum cut. This is a summary of main results of the thesis:
* A polynomial-time algorithm for k-VERTEX-COLORABILITY in the class of
P5-free graphs (for any fixed value k).
* A proof of NP-completeness of VERTEX- and EDGES_COLORABILITY in the class of graphs with girth at least g for any value of g ≥ 3.
* A polynomial-time algorithm for 3-VERTEX-COLORABILITY of (claw,hourglass)-free graphs and an extension of that result to an infinitely increasing family of subclasses of claw-free graphs.
* An exact algorithm for MAX-CUT running in time O*(2(1-2/Delta)n) in the class of graphs with maximum degree Delta.
* A proof of NP-completeness of MAX-CUT and MAX-BISECTION on unit disk graphs.
* A polynomial-time algorithm for k-VERTEX-COLORABILITY in the class of
P5-free graphs (for any fixed value k).
* A proof of NP-completeness of VERTEX- and EDGES_COLORABILITY in the class of graphs with girth at least g for any value of g ≥ 3.
* A polynomial-time algorithm for 3-VERTEX-COLORABILITY of (claw,hourglass)-free graphs and an extension of that result to an infinitely increasing family of subclasses of claw-free graphs.
* An exact algorithm for MAX-CUT running in time O*(2(1-2/Delta)n) in the class of graphs with maximum degree Delta.
* A proof of NP-completeness of MAX-CUT and MAX-BISECTION on unit disk graphs.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references (p. 57-61).
Subject
(authority = RUETD)
Topic
Operations Research
Subject
(authority = ETD-LCSH)
Topic
Graph algorithms
Subject
(authority = ETD-LCSH)
Topic
Graph coloring
Subject
(authority = ETD-LCSH)
Topic
Graph theory
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Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
Identifier
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.13472
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ETD_175
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doi:10.7282/T3J67HDC
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ETD doctoral
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Open
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Name
Marcin Kaminski
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Rutgers University. Graduate School-New Brunswick
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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