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COMPGEOM
2008
ACM
13 years 6 months ago
Extremal problems on triangle areas in two and three dimensions
The study of extremal problems on triangle areas was initiated in a series of papers by Erdos and Purdy in the early 1970s. In this paper we present new results on such problems, ...
Adrian Dumitrescu, Micha Sharir, Csaba D. Tó...
EOR
2010
178views more  EOR 2010»
13 years 4 months ago
Facility location problems in the plane based on reverse nearest neighbor queries
For a finite set of points S, the (monochromatic) Reverse Nearest Neighbor (RNN) rule associates with any query point q the subset of points in S that have q as its nearest neighb...
Sergio Cabello, José Miguel Díaz-B&a...
CCCG
2008
13 years 6 months ago
Computing the Stretch Factor of Paths, Trees, and Cycles in Weighted Fixed Orientation Metrics
Let G be a graph embedded in the L1-plane. The stretch factor of G is the maximum over all pairs of distinct vertices p and q of G of the ratio LG 1 (p, q)/L1(p, q), where LG 1 (p...
Christian Wulff-Nilsen
AUTOMATICA
2007
88views more  AUTOMATICA 2007»
13 years 4 months ago
Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence
In this paper, we generalize the notion of persistence, which has been originally introduced for two-dimensional formations, to Rd for d 3, seeking to provide a theoretical framew...
Changbin Yu, Julien M. Hendrickx, Baris Fidan, Bri...
ICRA
2000
IEEE
86views Robotics» more  ICRA 2000»
13 years 9 months ago
Randomized Planning for Short Inspection Paths
This paper addresses the following inspection problem: given a known workspace and a robot with vision capabilities compute a short path path for the robot such that each point on...
Tim Danner, Lydia E. Kavraki