Next century challenges: scalable coordination in sensor networks
MobiCom '99 Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Steinitz representations of polyhedra and the Colin de Verdiére number
Journal of Combinatorial Theory Series B
Geometric ad-hoc routing: of theory and practice
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Virtual coordinates for ad hoc and sensor networks
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Greedy drawings of triangulations
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum weight convex Steiner partitions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct Greedy Graph Drawing in the Hyperbolic Plane
Graph Drawing
Greedy routing with guaranteed delivery using Ricci flows
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
Succinct Greedy Geometric Routing in the Euclidean Plane
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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
A generalized greedy routing algorithm for 2-connected graphs
Theoretical Computer Science
GD'10 Proceedings of the 18th 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
Deterministic greedy routing with guaranteed delivery in 3D wireless sensor networks
MobiHoc '11 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing
Embedding stacked polytopes on a polynomial-size grid
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On succinct convex greedy drawing of 3-connected plane graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A lower bound on greedy embedding in euclidean plane
GPC'10 Proceedings of the 5th international conference on Advances in Grid and Pervasive Computing
Schnyder greedy routing algorithm
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Transactions on Computational Science XIV
Succinct greedy drawings do not always exist
GD'09 Proceedings of the 17th international conference on Graph Drawing
Monotone drawings of graphs with fixed embedding
GD'11 Proceedings of the 19th international conference on Graph Drawing
Shifting strategy for geometric graphs without geometry
Journal of Combinatorial Optimization
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
Space lower bounds for low-stretch greedy embeddings
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Link failure recovery technique for greedy routing in the hyperbolic plane
Computer Communications
GD'12 Proceedings of the 20th international conference on Graph Drawing
An optimal greedy routing algorithm for triangulated polygons
Computational Geometry: Theory and Applications
A simple routing algorithm based on Schnyder coordinates
Theoretical Computer Science
Greedy routing via embedding graphs onto semi-metric spaces
Theoretical Computer Science
Category-based routing in social networks: Membership dimension and the small-world phenomenon
Theoretical Computer Science
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We conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance to t decreases monotonically along the path. A consequence of this conjecture would be that in any ad hoc network containing such a graph as a spanning subgraph, two-dimensional virtual coordinates for the nodes can be found for which the method of purely greedy geographic routing is guaranteed to work. We discuss this conjecture and its equivalent forms show that its hypothesis is as weak as possible, and show a result delimiting the applicability of our approach: any 3-connected K3,3-free graph has a planar 3-connected spanning subgraph. We also present two alternative versions of greedy routing on virtual coordinates that provably work. Using Steinitz's theorem we show that any 3-connected planar graph can be embedded in three dimensions so that greedy routing works, albeit with a modified notion of distance; we present experimental evidence that this scheme can be implemented effectively in practice. We also present a simple but provably robust version of greedy routing that works for any graph with a 3-connected planar spanning subgraph.