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F. Thomson Leighton. Moitra, Ankur Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2010-03-25T15:31:20Z 2010-03-25T15:31:20Z 2009 2009 http://hdl.handle.net/1721.1/53323 550599596 Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009. Cataloged from PDF version of thesis. Includes bibliographical references (p. 32-33). Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, aid these coordinates are used to perform point-to-point routing. Here we resolve a conjecture of Papadimitrion and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Eulidean plane. This immediately implies that all 3-connected graphs that exclude K₃,₃ as a minor admit a greedy embedding into the Euclidean plane. Additionally, we provide the first non-trivial examples of graphs that admit no such embedding. These structural results provide efficiently verifiable certificates that a graph admits a greedy embedding or that a graph admits no greedy embedding into the Euclideau plane. by Ankur Moitra. S.M. 33 p. eng Massachusetts Institute of Technology 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. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. A solution to the Papadimitriou-Ratajczak conjecture Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="a23bf070-b595-42c4-a771-a0607dbe2d0d"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>A solution to the Papadimitriou-Ratajczak conjecture</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2009</PublicationDate> <Authors> <Author> <DisplayName>Moitra, Ankur</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, aid these coordinates are used to perform point-to-point routing. Here we resolve a conjecture of Papadimitrion and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Eulidean plane. This immediately implies that all 3-connected graphs that exclude K₃,₃ as a minor admit a greedy embedding into the Euclidean plane. Additionally, we provide the first non-trivial examples of graphs that admit no such embedding. These structural results provide efficiently verifiable certificates that a graph admits a greedy embedding or that a graph admits no greedy embedding into the Euclideau plane.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>