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» Crossing and Weighted Crossing Number of Near-Planar Graphs
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JACM
2007
115views more  JACM 2007»
13 years 7 months ago
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
We consider the problem of finding a shortest cycle (freely) homotopic to a given simple cycle on a compact, orientable surface. For this purpose, we use a pants decomposition of...
Éric Colin de Verdière, Francis Laza...
GD
2006
Springer
13 years 11 months ago
Planarity Testing and Optimal Edge Insertion with Embedding Constraints
The planarization method has proven to be successful in graph drawing. The output, a combinatorial planar embedding of the so-called planarized graph, can be combined with state-o...
Carsten Gutwenger, Karsten Klein, Petra Mutzel
DCG
2006
110views more  DCG 2006»
13 years 7 months ago
High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in Rn . It has recently been shown that properties of the centrosymmetric polytope P = AC are ...
David L. Donoho
FOCS
2006
IEEE
14 years 1 months ago
On a Geometric Generalization of the Upper Bound Theorem
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
Uli Wagner
ICOST
2007
Springer
14 years 1 months ago
Tracking People in Indoor Environments
Tracking the movement of people in indoor environments is useful for a variety of applications including elderly care, study of shopper behavior in shopping centers, security etc. ...
Candy Yiu, Suresh Singh