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dc.contributor.advisorF. Thomson Leighton.en_US
dc.contributor.authorMoitra, Ankuren_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2011-09-27T18:33:12Z
dc.date.available2011-09-27T18:33:12Z
dc.date.copyright2011en_US
dc.date.issued2011en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/66019
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (p. 125-129).en_US
dc.description.abstractSuppose we are given a gigantic communication network, but are only interested in a small number of nodes (clients). There are many routing problems we could be asked to solve for our clients. Is there a much smaller network - that we could write down on a sheet of paper and put in our pocket - that approximately preserves all the relevant communication properties of the original network? As we will demonstrate, the answer to this question is YES, and we call this smaller network a vertex sparsifier. In fact, if we are asked to solve a sequence of optimization problems characterized by cuts or flows, we can compute a good vertex sparsifier ONCE and discard the original network. We can run our algorithms (or approximation algorithms) on the vertex sparsifier as a proxy - and still recover approximately optimal solutions in the original network. This novel pattern saves both space (because the network we store is much smaller) and time (because our algorithms run on a much smaller graph). Additionally, we apply these ideas to obtain a master theorem for graph partitioning problems - as long as the integrality gap of a standard linear programming relaxation is bounded on trees, then the integrality gap is at most a logarithmic factor larger for general networks. This result implies optimal bounds for many well studied graph partitioning problems as a special case, and even yields optimal bounds for more challenging problems that had not been studied before. Morally, these results are all based on the idea that even though the structure of optimal solutions can be quite complicated, these solution values can be approximated by crude (even linear) functions.en_US
dc.description.statementofresponsibilityby Ankur Moitra.en_US
dc.format.extent129 p.en_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleVertex sparsification and universal rounding algorithmsen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
dc.identifier.oclc751987346en_US


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