A solution to the Papadimitriou-Ratajczak conjecture
Name
550599596-MIT.pdf
Description
Full printable version
Size
7.73 MB
Format
Adobe PDF
Checksum (MD5)
7e7d6f3602c00dcd6aa913f33324048e
Author(s)
Moitra, Ankur
Advisor(s)
F. Thomson Leighton.
Date Issued
2009
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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