TY - GEN

T1 - Greedy convex embeddings for Ad-Hoc networks

AU - Berchenko, Yakir

AU - Teicher, Mina

PY - 2009/12/1

Y1 - 2009/12/1

N2 - Recent advances in networked systems and wireless communications have set the stage for applications with wide-ranging benefits. Perhaps the most natural problem in such systems is the "efficient" propagation of locally stored data. In order to address this problem, the notion of greedy embedding was defined by Papadimitriou and Ratajczak [1], where the authors conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, the greedy embedding conjecture was proved by Leighton and Moitra [2]. However, their algorithm does not result in a drawing that is planar and convex in the Euclidean plane for all 3-connected planar graphs. Here we consider the planar convex greedy embedding conjecture and give a probabilistic proof for the existence of such embeddings. In addition, we discuss a second proof which is almost immediate in the case of an embedding into the 3-dimensional sphere.

AB - Recent advances in networked systems and wireless communications have set the stage for applications with wide-ranging benefits. Perhaps the most natural problem in such systems is the "efficient" propagation of locally stored data. In order to address this problem, the notion of greedy embedding was defined by Papadimitriou and Ratajczak [1], where the authors conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, the greedy embedding conjecture was proved by Leighton and Moitra [2]. However, their algorithm does not result in a drawing that is planar and convex in the Euclidean plane for all 3-connected planar graphs. Here we consider the planar convex greedy embedding conjecture and give a probabilistic proof for the existence of such embeddings. In addition, we discuss a second proof which is almost immediate in the case of an embedding into the 3-dimensional sphere.

KW - Convex embedding

KW - Greedy routing

KW - Planar graphs

UR - http://www.scopus.com/inward/record.url?scp=77951009496&partnerID=8YFLogxK

U2 - 10.1109/PDCAT.2009.68

DO - 10.1109/PDCAT.2009.68

M3 - Conference contribution

AN - SCOPUS:77951009496

SN - 9780769539140

T3 - Parallel and Distributed Computing, Applications and Technologies, PDCAT Proceedings

SP - 500

EP - 505

BT - 2009 International Conference on Parallel and Distributed Computing, Applications and Technologies, PDCAT 2009

T2 - 2009 International Conference on Parallel and Distributed Computing, Applications and Technologies, PDCAT 2009

Y2 - 8 December 2009 through 11 December 2009

ER -