Graph-theoretical conditions for inscribability and Delaunay realizability
Discrete Mathematics
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Computational Geometry: Theory and Applications
Online routing in geometric graphs
Online routing in geometric graphs
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Network sketching or: "How Much Geometry Hides in Connectivity?--Part II"
SODA '07 Proceedings of the eighteenth 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
On the efficiency of a local iterative algorithm to compute Delaunay realizations
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
A generalized greedy routing algorithm for 2-connected graphs
Theoretical Computer Science
Distributed computation of virtual coordinates for greedy routing in sensor networks
Discrete Applied Mathematics
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
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
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
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Sensor networks are emerging as a paradigm for future computing, but pose a number of challenges in the fields of networking and distributed computation. One challenge is to devise a greedy routing protocol -- one that routes messages through the network using only information available at a node or its neighbors. Modeling the connectivity graph of a sensor network as a 3-connected planar graph, we describe how to compute on the network in a distributed and local manner a special geometric embedding of the graph. This embedding supports a geometric routing protocol based on the "virtual" coordinates of the nodes derived from the embedding.