A solution to the Papadimitriou-Ratajczak conjecture
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 location...
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ndltd-MIT-oai-dspace.mit.edu-1721.1-533232019-05-02T16:14:52Z A solution to the Papadimitriou-Ratajczak conjecture Moitra, Ankur F. Thomson Leighton. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. 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. 2010-03-25T15:31:20Z 2010-03-25T15:31:20Z 2009 2009 Thesis http://hdl.handle.net/1721.1/53323 550599596 eng 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 33 p. application/pdf Massachusetts Institute of Technology |
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Electrical Engineering and Computer Science. Moitra, Ankur A solution to the Papadimitriou-Ratajczak conjecture |
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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. |
author2 |
F. Thomson Leighton. |
author_facet |
F. Thomson Leighton. Moitra, Ankur |
author |
Moitra, Ankur |
author_sort |
Moitra, Ankur |
title |
A solution to the Papadimitriou-Ratajczak conjecture |
title_short |
A solution to the Papadimitriou-Ratajczak conjecture |
title_full |
A solution to the Papadimitriou-Ratajczak conjecture |
title_fullStr |
A solution to the Papadimitriou-Ratajczak conjecture |
title_full_unstemmed |
A solution to the Papadimitriou-Ratajczak conjecture |
title_sort |
solution to the papadimitriou-ratajczak conjecture |
publisher |
Massachusetts Institute of Technology |
publishDate |
2010 |
url |
http://hdl.handle.net/1721.1/53323 |
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AT moitraankur asolutiontothepapadimitriouratajczakconjecture AT moitraankur solutiontothepapadimitriouratajczakconjecture |
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1719036955875868672 |