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
