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» Plane embeddings of planar graph metrics
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GD
2009
Springer
15 years 11 months ago
Manhattan-Geodesic Embedding of Planar Graphs
In this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains o...
Bastian Katz, Marcus Krug, Ignaz Rutter, Alexander...
KIVS
2011
Springer
14 years 9 months ago
A Feasibility Check for Geographical Cluster Based Routing under Inaccurate Node Localization in Wireless Sensor Networks
Localized geographic single path routing along a wireless network graph requires exact location information about the network nodes to assure message delivery guarantees. Node loc...
Hannes Frey, Ranjith Pillay
GD
2007
Springer
16 years 24 days ago
Simultaneous Geometric Graph Embeddings
We consider the following problem known as simultaneous geometric graph embedding (SGE). Given a set of planar graphs on a shared vertex set, decide whether the vertices can be pla...
Alejandro Estrella-Balderrama, Elisabeth Gassner, ...
DCG
2011
15 years 1 months ago
Small Grid Embeddings of 3-Polytopes
We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by O(27.55n ) = O(18...
Ares Ribó Mor, Günter Rote, Andr&eacut...
STOC
2009
ACM
171views Algorithms» more  STOC 2009»
16 years 7 months ago
On the geometry of graphs with a forbidden minor
We study the topological simplification of graphs via random embeddings, leading ultimately to a reduction of the Gupta-Newman-Rabinovich-Sinclair (GNRS) L1 embedding conjecture t...
James R. Lee, Anastasios Sidiropoulos