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Partitioning problems in discrete and computational geometry

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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Partitioning problems in discrete and computational geometry
SubTitle
PartName
PartNumber
NonSort
Identifier (displayLabel = ); (invalid = )
ETD_2315
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000052168
Language (objectPart = )
LanguageTerm (authority = ISO639-2); (type = code)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Computer Science
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Discrete geometry
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Geometry--Data processing
Abstract
Many interesting problems in Discrete and Computational Geometry involve partitioning. A main question is whether a given set, or sets, may be separated into parts satisfying certain properties. Sometime we also need to find an efficient way to do it - in other words an algorithm. In this thesis, we discuss several of problems and results of this kind.
First we give a combinatorial proof of the existence and the uniqueness of the generalized ham-sandwich cut for well separated point sets in R^d, that have the weak general position property. The combinatorial proof allows us to derive an O(n(log n)^d−3) running time algorithm to find a generalized cut for d given well separated point sets in R^d.
A second problem concerns the 6-way partition of a given convex set in R^2 using 3 lines. We reopen an old question and show that when the direction of one line is fixed, there is unique partition such that 6 regions have the same area.
In the Voronoi game two players A and B each play n points in a compact set S in R^d. They obtain scores equal to the total volume of the Voronoi cells of their points. There are one round and alternating versions of the game. We give the player A's best strategy to minimize the area of player B's one(first) Voronoi cell.
PhysicalDescription
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electronic resource
Extent
viii, 65 p. : ill.
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Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 62-64)
Note (type = statement of responsibility)
by Jihui Zhao
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Zhao
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Jihui
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1971-
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Jihui Zhao
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Steiger
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William
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chair
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William Steiger
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Szegedy
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Mario
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internal member
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Mario Szegedy
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Kalantari
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Bahman
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Bahman Kalantari
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Bárány
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Imre
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outside member
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Advisory Committee
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Imre Bárány
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2010
DateOther (qualifier = exact); (type = degree)
2010-01
Place
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xx
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
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ETD
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Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3X34XM8
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work.
Copyright
Status
Copyright protected
Notice
Note
Availability
Status
Open
Reason
Permission or license
Note
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Zhao
GivenName
Jihui
Role
Copyright Holder
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
Label
Place
DateTime
2009-12-17 16:57:16
Detail
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Name
Jihui Zhao
Affiliation
Rutgers University. Graduate School - New Brunswick
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License
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Author Agreement License
Detail
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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ETD
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application/pdf
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