RUcore: Rutgers University Community Repository
Some problems on discrete geometry and combinatorics
Descriptive
TitleInfo
Title
Some problems on discrete geometry and combinatorics
Name
(type = personal)
NamePart
(type = family)
Wang
NamePart
(type = given)
Lei
NamePart
(type = date)
1978-
DisplayForm
Lei Wang
Role
RoleTerm
(authority = RULIB)
author
Name
(type = personal)
NamePart
(type = family)
Szegedy
NamePart
(type = given)
Mario
DisplayForm
Mario Szegedy
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
chair
Name
(type = personal)
NamePart
(type = family)
Steiger
NamePart
(type = given)
William
DisplayForm
William Steiger
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
co-chair
Name
(type = personal)
NamePart
(type = family)
Kalantari
NamePart
(type = given)
Bahman
DisplayForm
Bahman Kalantari
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Aronov
NamePart
(type = given)
Boris
DisplayForm
Boris Aronov
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
outside member
Name
(type = corporate)
NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
(type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm
(authority = RULIB)
school
TypeOfResource
Text
Genre
(authority = marcgt)
theses
OriginInfo
DateCreated
(qualifier = exact)
2012
DateOther
(qualifier = exact);
(type = degree)
2012-01
CopyrightDate
(qualifier = exact)
2012
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
(authority = ISO639-2b);
(type = code)
eng
Abstract
(type = abstract)
Let K be a convex body in the plane. It is known that K can never be partitioned into seven regions of equal area by three non-concurrent lines. We will be concerned with a partition of K by three non-concurrent lines such that the ratio of the area of smallest region to the area of biggest region is maximum. We call this an optimal balanced partition at K. We show that the best possible ratio is achieved when K is a triangle and we characterize the optimal balanced partition in this case. We conjecture that the condition holds for optimal balanced partitions of all convex bodies but can only prove a weaker result. In the second part of the thesis, we switch to the zigzag problem. We are given a set of n points in R² and seek the minimum number of line segments required for a polygonal chain (or a simple polygonal chain) to traverse all the points. We show an n/2 + O(n/log{n}) upper bound if self-intersection is allowed and an n - [n-2/8] upper bound if self-intersection is not allowed. The third part of this thesis is about finding the optimally balanced forward degree sequence of a graph. The final part studies the optimal solutions for some variants of the Towers of Hanoi problem.
Subject
(authority = RUETD)
Topic
Computer Science
Subject
(authority = ETD-LCSH)
Topic
Combinatorial analysis
Subject
(authority = ETD-LCSH)
Topic
Discrete geometry
Subject
(authority = ETD-LCSH)
Topic
Partitions (Mathematics)
RelatedItem
(type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
RelatedItem
(type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
(type = local)
rucore19991600001
Identifier
ETD_3753
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000064188
PhysicalDescription
Form
(authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vii, 74 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Lei Wang
Location
PhysicalLocation
(authority = marcorg);
(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3P55M3Q
Genre
(authority = ExL-Esploro)
ETD doctoral
Back to the top
Rights
RightsDeclaration
(ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder
(type = personal)
Name
FamilyName
Wang
GivenName
Lei
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
(encoding = w3cdtf);
(qualifier = exact);
(point = start)
2011-12-23 01:54:17
AssociatedEntity
Name
Lei Wang
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Back to the top
Technical
FileSize
(UNIT = bytes)
782848
OperatingSystem
(VERSION = 5.1)
windows xp
ContentModel
ETD
MimeType
(TYPE = file)
application/pdf
MimeType
(TYPE = container)
application/x-tar
FileSize
(UNIT = bytes)
788480
Checksum
(METHOD = SHA1)
386866229c55f272bb4d3bbcc92df9d53bf45a42
Back to the top
Statistical Profile