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COMPGEOM
2010
ACM
13 years 11 months ago
Tangencies between families of disjoint regions in the plane
Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the memb...
János Pach, Andrew Suk, Miroslav Treml
CORR
2006
Springer
103views Education» more  CORR 2006»
13 years 7 months ago
Pants Decomposition of the Punctured Plane
A pants decomposition of an orientable surface is a collection of simple cycles that partition into pants, i.e., surfaces of genus zero with three boundary cycles. Given a set P...
Sheung-Hung Poon, Shripad Thite
AAIM
2009
Springer
119views Algorithms» more  AAIM 2009»
14 years 2 months ago
Link Distance and Shortest Path Problems in the Plane
We develop algorithms to compute Voronoi diagrams, shortest path maps, and the Fr´echet distance in the plane with polygonal obstacles. Distances between points are measured eithe...
Atlas F. Cook, Carola Wenk
CCCG
2010
13 years 9 months ago
Maximum geodesic routing in the plane with obstacles
Do convex obstacles in the plane always leave 3 separate escape routes? Here, an escape route is a locally geodesic path that avoids the obstacles; escape routes are separate if t...
David L. Millman, Matthew O'Meara, Jack Snoeyink, ...
STACS
2010
Springer
14 years 2 months ago
Long Non-crossing Configurations in the Plane
We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computation...
Noga Alon, Sridhar Rajagopalan, Subhash Suri