A Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds

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atmire.migration.oldid4999
dc.contributor.advisorLi, Zongpeng
dc.contributor.authorFang, Wei
dc.contributor.committeememberHoyer, Peter Christian
dc.contributor.committeememberNiu, Di
dc.date.accessioned2016-09-29T15:25:35Z
dc.date.available2016-09-29T15:25:35Z
dc.date.issued2016
dc.date.submitted2016en
dc.description.abstractNetwork coding encourages information mixing at the intermediate nodes within a network. The multiple-unicast conjecture proposed by Li and Li [18] in 2004 is one of the most well-known unsolved problems in network coding field. The conjecture asserts that, for multiple independent unicast transmissions in an undirected network, network coding has no advantage over traditional routing. In this thesis, we study the conjecture by embedding graphs into Riemannian manifolds using a geometric framework developed by Xiahou el al. [32]. We prove that isometric embedding of graphs into a Riemannian manifold is impossible. Then, interestingly, we construct an embedding that achieves an infinitesimally small distortion. We show that if the multiple-unicast network coding conjecture is true on Riemannian manifolds, it is also true for undirected networks. Our hope is to develop a Riemannian geometry approach for making new progresses against the long-time open conjecture.en_US
dc.identifier.citationFang, W. (2016). A Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25044en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/25044
dc.identifier.urihttp://hdl.handle.net/11023/3351
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectComputer Science
dc.subject.classificationnetwork codingen_US
dc.subject.classificationmultiple-unicast conjectureen_US
dc.subject.classificationRiemannian manifoldsen_US
dc.titleA Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds
dc.typemaster thesis
thesis.degree.disciplineComputer Science
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.item.requestcopytrue
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