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» Crossing and Weighted Crossing Number of Near-Planar Graphs
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JACM
2007
115views more  JACM 2007»
14 years 9 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
15 years 1 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»
14 years 9 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
15 years 3 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
93
Voted
ICOST
2007
Springer
15 years 3 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