Succinct Greedy Graph Drawing in the Hyperbolic Plane

Authors:
David Eppstein;Michael T. Goodrich
Affiliations:
Computer Science Department, University of California, Irvine, USA;Computer Science Department, University of California, Irvine, USA
Venue:
Graph Drawing
Year:
2009

Citing 16
Cited 7

On finding lowest common ancestors: simplification and parallelization

SIAM Journal on Computing
A data structure for dynamic trees

Journal of Computer and System Sciences
Embedding planar graphs on the grid

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
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
Asymptotically optimal geometric mobile ad-hoc routing

DIALM '02 Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications
Finding Cores of Limited Length

WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Worst-Case optimal and average-case efficient geometric ad-hoc routing

Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
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
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
On the efficiency of a local iterative algorithm to compute Delaunay realizations

WEA'08 Proceedings of the 7th international conference on Experimental algorithms

Succinct Greedy Geometric Routing in the Euclidean Plane

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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
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
Revisiting hyperbolic voronoi diagrams in two and higher dimensions from theoretical, applied and generalized viewpoints

Transactions on Computational Science XIV
Succinct greedy drawings do not always exist

GD'09 Proceedings of the 17th international conference on Graph Drawing
Low distortion delaunay embedding of trees in hyperbolic plane

GD'11 Proceedings of the 19th international conference on Graph Drawing

Quantified Score

Hi-index	0.00

Visualization

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.