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Property testing, PCPs and CSPs

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TitleInfo
Title
Property testing, PCPs and CSPs
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Bhangale
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Amey
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1990-
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Amey Bhangale
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Swastik
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Swastik Kopparty
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Advisory Committee
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chair
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Shubhangi
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Shubhangi Saraf
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internal member
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Szegedy
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Mario
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Mario Szegedy
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Advisory Committee
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Raghavendra
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Prasad
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Prasad Raghavendra
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Advisory Committee
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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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2017
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2017-05
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2017
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xx
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eng
Abstract (type = abstract)
Many optimization problems can be modeled as constraint satisfaction problems (CSPs). Hence understanding the complexity of solving or approximating CSPs is a fundamental problem in computer science. The famous PCP (probabilistically checkable proof) Theorem states that certain CSPs are hard to approximate within a constant factor. In the language of proof verification, the theorem implies that a proof of a mathematical statement can be written in a specific format such that it allows an sublinear time verification of the proof. Thus, property testing procedures are central to PCPs, and in fact the proof of the PCP theorem involves many interesting property testing algorithms. Some of the highlights of this dissertation include the following results: 1. Low degree testing is one of the important components in the proof of the PCP theorem and Dictatorship testing is central in proving hardness of approximation results. This thesis presents a Cube vs Cube low degree test which has significantly better parameters than the previously known tests. We also improve on the soundness of k-bit dictatorship test with perfect completeness. 2. In the area of inapproximability, this thesis offers a complete characterization of approximating the covering number of a CSP, assuming a covering variant of Unique Games Conjecture. We also prove tight inapproximability results for Bi-Covering problem. 3. This thesis studies CSPs from a multi-objective point of view. We give almost optimal approximation algorithms for multi-objective Max-CSP (simultaneous CSPs), and also prove inapproximability results.
Subject (authority = local)
Topic
Property Testing
Subject (authority = RUETD)
Topic
Computer Science
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Rutgers University Electronic Theses and Dissertations
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ETD_7916
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (viii, 277 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Subject (authority = ETD-LCSH)
Topic
Mathematical optimization
Subject (authority = ETD-LCSH)
Topic
Constraint programming (Computer science)
Note (type = statement of responsibility)
by Amey Bhangale
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Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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Identifier (type = doi)
doi:10.7282/T3J67KQ7
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

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The author owns the copyright to this work.
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Name
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Bhangale
GivenName
Amey
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Permission or license
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2017-03-30 16:20:25
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Amey Bhangale
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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.
Copyright
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Copyright protected
Availability
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Open
Reason
Permission or license
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2017-03-30T16:19:01
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