{"id":{"repo_id":"calgary","oai_identifier":"oai:ucalgary.scholaris.ca:11023/3351"},"canonical_url":"https://search.dev.ndltd.org/etd/calgary/oai:ucalgary.scholaris.ca:11023/3351","repository":{"repo_id":"calgary","name":"University of Calgary","base_url":"https://ucalgary.scholaris.ca/server/oai/request"},"display":{"title":"A Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds","abstract":"Network 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.","abstract_html":"Network 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.","abstract_has_math":false,"creators":["Fang, Wei"],"institution":"Graduate Studies","degree_name":"Master of Science (MSc)","degree_level":null,"degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":["Li, Zongpeng"],"committee_chairs":[],"committee_members":["Hoyer, Peter Christian","Niu, Di"],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-24T01:30:44Z","subjects":["Computer Science"],"languages":["eng"],"rights":["University 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."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["http://dx.doi.org/10.11575/PRISM/25044"],"render_values":[{"text":"http://dx.doi.org/10.11575/PRISM/25044","href":"http://dx.doi.org/10.11575/PRISM/25044","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/11023/3351","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Li, Zongpeng"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Hoyer, Peter Christian","Niu, Di"]},{"key":"dc:creator","label":"Author","values":["Fang, Wei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-09-29T15:25:35Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-09-29T15:25:35Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Calgary"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Calgary"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["University 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."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["http://dx.doi.org/10.11575/PRISM/25044"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11023/3351"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Network 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."]},{"key":"dc:title","label":"Title","values":["A Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds"]}]}],"canonical_facts":{"dc:contributor.advisor":["Li, Zongpeng"],"dc:contributor.committeemember":["Hoyer, Peter Christian","Niu, Di"],"dc:creator":["Fang, Wei"],"dc:date.accessioned":["2016-09-29T15:25:35Z"],"dc:date.available":["2016-09-29T15:25:35Z"],"dc:date.issued":["2016"],"dc:description.abstract":["Network 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."],"dc:identifier.doi":["http://dx.doi.org/10.11575/PRISM/25044"],"dc:identifier.uri":["http://hdl.handle.net/11023/3351"],"dc:language.iso":["eng"],"dc:publisher.institution":["University of Calgary"],"dc:rights":["University 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:subject":["Computer Science"],"dc:title":["A Study of the Multiple-Unicast Network Coding Conjecture Using Riemannian Manifolds"],"dc:type":["master thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["University of Calgary"]},"updated_at":"2026-07-24T01:30:44Z"}