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New computational aspects of discrepancy theory

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TitleInfo
Title
New computational aspects of discrepancy theory
Name (type = personal)
NamePart (type = family)
Nikolov
NamePart (type = given)
Aleksandar
NamePart (type = date)
1985-
DisplayForm
Aleksandar Nikolov
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Muthukrishnan
NamePart (type = given)
S.
DisplayForm
S. Muthukrishnan
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Saks
NamePart (type = given)
Michael
DisplayForm
Michael Saks
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Kopparty
NamePart (type = given)
Swastik
DisplayForm
Swastik Kopparty
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Vadhan
NamePart (type = given)
Salil
DisplayForm
Salil Vadhan
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)
2014
DateOther (qualifier = exact); (type = degree)
2014-10
CopyrightDate (encoding = w3cdtf)
2014
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
The main focus of this thesis work is computational aspects of discrepancy theory. Discrepancy theory studies how well discrete objects can approximate continuous ones. This question is ubiquitous in mathematics and computer science, and discrepancy theory has found numerous applications. In this thesis work, we (1) initiate the study of the polynomial time approximability of central discrepancy measures: we prove the first hardness of approximation results and design the first polynomial time approximation algorithms for combinatorial and hereditary discrepancy. We also (2) make progress on longstanding open problems in discrepancy theory, using insights from computer science: we give nearly tight hereditary discrepancy lower bounds for axis-aligned boxes in higher dimensions, and for homogeneous arithmetic progressions. Finally, we have (3) found new applications of discrepancy theory to (3a) fundamental questions in private data analysis and to (3b) communication complexity. In particular, we use discrepancy theory to design nearly optimal efficient algorithms for counting queries, in all parameter regimes considered in the literature. We also show that discrepancy lower bounds imply communication lower bounds for approximation problems in the one-way model. Directions for further research and connections to expander graphs, compressed sensing, and the design of approximation algorithms are outlined.
Subject (authority = RUETD)
Topic
Computer Science
Subject (authority = ETD-LCSH)
Topic
Irregularities of distribution (Number theory)
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5939
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (ix, 172 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Aleksandar Nikolov
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3RN3749
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Nikolov
GivenName
Aleksandar
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-09-29 10:18:51
AssociatedEntity
Name
Aleksandar Nikolov
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
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Technical

RULTechMD (ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem (VERSION = 5.1)
windows xp
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