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
Bounded Degree Spanning Trees (Extended Abstract)
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Graph Theory With Applications
Graph Theory With Applications
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
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
Greedy drawings of triangulations
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Some Results on Greedy Embeddings in Metric Spaces
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
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 succinct convex greedy drawing of 3-connected plane graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
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In this paper, we generalize the greedy routing concept to use semi-metric spaces. We prove that any connected n-vertex tree T admits a greedy embedding, onto an appropriate semi-metric space such that (1) each vertex v of the tree is represented by k=deg(v) virtual coordinates (where the numbers are from 1 to 2n-2); and (2) using an appropriate distance definition, the unique simple path between any two vertices in T is always a distance decreasing path between the two vertices. Applying the result to an arbitrary connected graph G, such a greedy embedding of any of its spanning tree T onto a semi-metric space becomes a greedy embedding of G onto the same semi-metric space. In particular, for 3-connected plane graphs, we prove that, for a 3-connected plane graph G, there is a greedy embedding of G such that: (1) the greedy embedding can be obtained in linear time; (2) each vertex can be represented by at most 3 virtual coordinates from 1 to 2n-2; and (3) the distance between two vertices can be computed in constant time. To our best knowledge, this is the first greedy routing algorithm for 3-connected plane graphs, albeit with non-standard notions of greedy embedding and greedy routing, such that: (1) it runs in linear time to compute the virtual coordinates for the vertices; and (2) the virtual coordinates are represented succinctly in O(logn) bits.