Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Internetworking with TCP/IP, Volume 1: Principles, Protocols, and Architectures, Fourth Edition
Internetworking with TCP/IP, Volume 1: Principles, Protocols, and Architectures, Fourth Edition
Computer Networks
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Topological hole detection in wireless sensor networks and its applications
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
Convex Drawings of 3-Connected Plane Graphs
Algorithmica
Distributed computation of virtual coordinates
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A Distributed Geometric Routing Algorithm for Ad HocWireless Networks
ITNG '07 Proceedings of the International Conference on Information Technology
Schnyder Woods and Orthogonal Surfaces
Discrete & Computational Geometry
Some Results on Greedy Embeddings in Metric Spaces
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Schnyder Woods for Higher Genus Triangulated Surfaces, with Applications to Encoding
Discrete & Computational Geometry - Special Issue: 24th Annual Symposium on Computational Geometry
Succinct Greedy Geometric Routing in the Euclidean Plane
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Greedy Drawings of Triangulations
Discrete & Computational Geometry
On Succinctness of Geometric Greedy Routing in Euclidean Plane
ISPAN '09 Proceedings of the 2009 10th International Symposium on Pervasive Systems, Algorithms, and Networks
Greedy Convex Embeddings for Sensor Networks
PDCAT '09 Proceedings of the 2009 International Conference on Parallel and Distributed Computing, Applications and Technologies
On the efficiency of a local iterative algorithm to compute Delaunay realizations
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
On convex greedy embedding conjecture for 3-connected planar graphs
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Schnyder greedy routing algorithm
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Succinct greedy drawings do not always exist
GD'09 Proceedings of the 17th international conference on Graph Drawing
Greedy routing via embedding graphs onto semi-metric spaces
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Competitive routing in the half-θ6-graph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Succinct strictly convex greedy drawing of 3-connected plane graphs
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
GD'12 Proceedings of the 20th international conference on Graph Drawing
A simple routing algorithm based on Schnyder coordinates
Theoretical Computer Science
Greedy routing via embedding graphs onto semi-metric spaces
Theoretical Computer Science
Hi-index | 0.00 |
Geometric routing by using virtual locations is an elegant way for solving network routing problems. In its simplest form, greedy routing, a message is simply for warded to a neighbor that is closer to the destination. It has been an open conjecture whether every 3-connected plane graph has a greedy drawing in R2 (by Papadimitriou and Ratajczak [23]). Leighton and Moitra [20] recently settled this conjecture positively. One main drawback of this approach is that the coordinates of the virtual locations requires Ω(n log n) bits to represent (the same space usage as traditional routing table approaches). This makes greedy routing infeasible in applications. A similar result was obtained by Angelini et al. [2]. However, neither of the two papers give the time efficiency analysis of their algorithms. In addition, as pointed out in [16], the drawings in these two papers are not necessarily planar nor convex. In this paper, we show that the classical Schnyder drawing in R2 of plane triangulations is greedy with respect to a simple natural metric function H(u, v) over R2 that is equivalent to Euclidean metric DE(u, v) (in the sense that DE(u, v) DE(u, v).) The drawing is succinct, using two integer coordinates between 0 and 2n − 5. For 3-connected plane graphs, there is another conjecture by Papadimitriou and Ratajczak (as stated in [16]): Convex Greedy Embedding Conjecture: Every 3-connected planar graph has a convex greedy embedding in the Euclidean plane. In a recent paper [6], Cao et al. provided a plane graph G and showed that any convex greedy embedding of G in Euclidean plane must use Ω(n)-bit coordinates Thus, if we add the succinctness requirement, the Convex Greedy Embedding Conjecture is false. In this paper, we show that the classical Schnyde drawing in R2 of 3-connected plane graphs is weakly greedy with respect to the same metric function H(*, *). The drawing is planar, convex, and succinct, using two integer coordinates between 0 and f (where f is the number of internal faces of G).