<?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="static/style.xsl"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-09-23T17:31:04Z</responseDate><request verb="GetRecord" identifier="oai:dspace.mit.edu:1721.1/88906" metadataPrefix="dim">https://dspace.mit.edu/server/oai/request</request><GetRecord><record><header><identifier>oai:dspace.mit.edu:1721.1/88906</identifier><datestamp>2026-06-06T00:54:47Z</datestamp><setSpec>com_1721.1_7582</setSpec><setSpec>com_1721.1_7581</setSpec><setSpec>col_1721.1_131023</setSpec></header><metadata><dim:dim xmlns:dim="http://www.dspace.org/xmlns/dspace/dim" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:doc="http://www.lyncode.com/xoai" xsi:schemaLocation="http://www.dspace.org/xmlns/dspace/dim http://www.dspace.org/schema/dim.xsd">
   <dim:field mdschema="dc" element="contributor" qualifier="advisor" lang="en_US">Michel Goemans.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="author" lang="en_US">Oliveira, Rafael (Rafael Mendes de Oliveira)</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="other" lang="en_US">Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="department">Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="accessioned">2014-08-19T17:36:46Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="available">2014-08-19T17:36:46Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="copyright" lang="en_US">2012</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="issued" lang="en_US">2012</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="uri">http://hdl.handle.net/1721.1/88906</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="oclc" lang="en_US">884275927</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2012.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Cataloged from PDF version of thesis.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Includes bibliographical references (page 31).</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="abstract" lang="en_US">We provide results of intensive experimental data in order to investigate the existence of spectrally thin trees and unweighted spectral sparsifiers for graphs with small expansion. In addition, we also survey and prove some partial results on the existence of spectrally thin trees on dense graphs with high enough expansion.</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="statementofresponsibility" lang="en_US">by Rafael Oliveira.</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="degree" lang="en_US">M.Eng.</dim:field>
   <dim:field mdschema="dc" element="format" qualifier="extent" lang="en_US">31 pages</dim:field>
   <dim:field mdschema="dc" element="language" qualifier="iso" lang="en_US">eng</dim:field>
   <dim:field mdschema="dc" element="publisher" lang="en_US">Massachusetts Institute of Technology</dim:field>
   <dim:field mdschema="dc" element="rights" lang="en_US">M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.</dim:field>
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   <dim:field mdschema="dc" element="subject" lang="en_US">Electrical Engineering and Computer Science.</dim:field>
   <dim:field mdschema="dc" element="title" lang="en_US">Spectral sparsification and spectrally thin trees</dim:field>
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   	&lt;Title>Spectral sparsification and spectrally thin trees&lt;/Title>
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   	&lt;PublicationDate>2012&lt;/PublicationDate>
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        	&lt;DisplayName>Oliveira, Rafael (Rafael Mendes de Oliveira)&lt;/DisplayName>
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    &lt;Keyword>Electrical Engineering and Computer Science.&lt;/Keyword>
   	&lt;Abstract>We provide results of intensive experimental data in order to investigate the existence of spectrally thin trees and unweighted spectral sparsifiers for graphs with small expansion. In addition, we also survey and prove some partial results on the existence of spectrally thin trees on dense graphs with high enough expansion.&lt;/Abstract>
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