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» On simultaneous planar graph embeddings
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PAMI
2006
141views more  PAMI 2006»
13 years 6 months ago
Diffusion Maps and Coarse-Graining: A Unified Framework for Dimensionality Reduction, Graph Partitioning, and Data Set Parameter
We provide evidence that non-linear dimensionality reduction, clustering and data set parameterization can be solved within one and the same framework. The main idea is to define ...
Stéphane Lafon, Ann B. Lee
ISSAC
2007
Springer
146views Mathematics» more  ISSAC 2007»
14 years 25 days ago
Fast and exact geometric analysis of real algebraic plane curves
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...
Arno Eigenwillig, Michael Kerber, Nicola Wolpert
WADS
2005
Springer
111views Algorithms» more  WADS 2005»
14 years 5 days ago
On Geometric Dilation and Halving Chords
Let G be an embedded planar graph whose edges may be curves. The detour between two points, p and q (on edges or vertices) of G, is the ratio between the shortest path in G between...
Adrian Dumitrescu, Annette Ebbers-Baumann, Ansgar ...
DCG
2007
102views more  DCG 2007»
13 years 6 months ago
How to Exhibit Toroidal Maps in Space
Steinitz’s Theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of ...
Dan Archdeacon, C. Paul Bonnington, Joanna A. Elli...
INFOCOM
2007
IEEE
14 years 1 months ago
Face Tracing Based Geographic Routing in Nonplanar Wireless Networks
— Scalable and efficient routing is a main challenge in the deployment of large ad hoc wireless networks. An essential element of practical routing protocols is their accommodat...
Fenghui Zhang, Hao Li, Anxiao Jiang, Jianer Chen, ...