Succinct Greedy Graph Drawing in the Hyperbolic Plane
David Eppstein,Michael T. Goodrich +1 more
- pp 14-25
TLDR
A method for producing a greedy embedding of any n -vertex simple graph G in the hyperbolic plane, so that a message M between any pair of vertices may be routed by having each vertex that receives M pass it to a neighbor that is closer to M 's destination.Abstract:
We describe a method for producing a greedy embedding of any n -vertex simple graph G in the hyperbolic plane, so that a message M between any pair of vertices may be routed by having each vertex that receives M pass it to a neighbor that is closer to M 's destination. Our algorithm produces succinct drawings, where vertex positions are represented using O (logn ) bits and distance comparisons may be performed efficiently using these representations.read more
Citations
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Book ChapterDOI
Low distortion delaunay embedding of trees in hyperbolic plane
TL;DR: It is shown that any tree can be realized as the Delaunay graph of its embedded vertices, which implies useful properties such as guaranteed greedy routing and realization as minimum spanning trees.
Proceedings ArticleDOI
Greedy routing with guaranteed delivery using Ricci flows
TL;DR: This paper proposes to use conformal mapping to compute a new embedding of the sensor nodes in the plane such that greedy forwarding with the virtual coordinates guarantees delivery, and extracts a planar triangulation of the sensors with non-triangular faces as holes.
Journal ArticleDOI
Some Results on Greedy Embeddings in Metric Spaces
Tom Leighton,Ankur Moitra +1 more
TL;DR: This work resolves a conjecture of Papadimitriou and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Euclidean plane and proves a combinatorial condition that guarantees nonembeddability.
Proceedings ArticleDOI
Greedy Routing with Bounded Stretch
TL;DR: A polynomial-time algorithm that embeds combinatorial unit disk graphs (CUDGs) into O(log 2 n)- dimensional space, permitting greedy routing with constant stretch, which yields the best known stretch-space trade-off for compact routing on CUDGs.
Proceedings ArticleDOI
Some Results on Greedy Embeddings in Metric Spaces
Ankur Moitra,Tom Leighton +1 more
TL;DR: This work resolves a conjecture of Papadimitriou and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Euclidean plane and provides the first non-trivial examples of graphs that admit no such embedding.
References
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Proceedings ArticleDOI
GPSR: greedy perimeter stateless routing for wireless networks
Brad Karp,Hsiang-Tsung Kung +1 more
TL;DR: Greedy Perimeter Stateless Routing is presented, a novel routing protocol for wireless datagram networks that uses the positions of routers and a packet's destination to make packet forwarding decisions and its scalability on densely deployed wireless networks is demonstrated.
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TL;DR: An internationally best-selling, conceptual introduction to the TCP/IP protocols and Internetworking, this book interweaves a clear discussion of fundamentals and scientific principles with details and examples drawn from the latest technologies.
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Routing with guaranteed delivery in ad hoc wireless networks
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A data structure for dynamic trees
TL;DR: An O(mn log n)-time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse graphs.
Proceedings Article
Compass routing on geometric networks.
TL;DR: A close look at maps of numerous cities around the world, show that the previous way to explore a new, and unknown city will in general yield walks that will be close to the optimal ones to travel from one location to another.