On Computing the Diameter of a Point Set in High Dimensional Euclidean Space

1999 ◽  
pp. 366-377 ◽  
Author(s):  
Daniele V. Finocchiaro ◽  
Marco Pellegrini
Keyword(s):  
Euclidean Space ◽  
High Dimensional ◽  
Dimensional Euclidean Space ◽  
Point Set

scholarly journals On computing the diameter of a point set in high dimensional Euclidean space

2002 ◽  
Vol 287 (2) ◽  
pp. 501-514 ◽  
Author(s):  
Daniele V. Finocchiaro ◽  
Marco Pellegrini
Keyword(s):  
Euclidean Space ◽  
High Dimensional ◽  
Dimensional Euclidean Space ◽  
Point Set

scholarly journals Homology of moduli spaces of linkages in high-dimensional Euclidean space

2013 ◽  
Vol 13 (2) ◽  
pp. 1183-1224 ◽  
Author(s):  
Dirk Schütz
Keyword(s):  
Euclidean Space ◽  
Moduli Spaces ◽  
High Dimensional ◽  
Dimensional Euclidean Space

scholarly journals Reflection-Like Maps in High-Dimensional Euclidean Space

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 872
Author(s):  
Zhiyong Huang ◽  
Baokui Li
Keyword(s):  
Euclidean Space ◽  
Convex Domain ◽  
Orthogonal Transformation ◽  
High Dimensional ◽  
Dimensional Euclidean Space ◽  
Local Domain ◽  
Euclidean Spaces ◽  
Line Cross ◽  
Klein Model

In this paper, we introduce reflection-like maps in n-dimensional Euclidean spaces, which are affinely conjugated to θ : ( x 1 , x 2 , … , x n ) → 1 x 1 , x 2 x 1 , … , x n x 1 . We shall prove that reflection-like maps are line-to-line, cross ratios preserving on lines and quadrics preserving. The goal of this article was to consider the rigidity of line-to-line maps on the local domain of R n by using reflection-like maps. We mainly prove that a line-to-line map η on any convex domain satisfying η ∘ 2 = i d and fixing any points in a super-plane is a reflection or a reflection-like map. By considering the hyperbolic isometry in the Klein Model, we also prove that any line-to-line bijection f : D n ↦ D n is either an orthogonal transformation, or a composition of an orthogonal transformation and a reflection-like map, from which we can find that reflection-like maps are important elements and instruments to consider the rigidity of line-to-line maps.

scholarly journals Reporting Neighbors in High-Dimensional Euclidean Space

2014 ◽  
Vol 43 (4) ◽  
pp. 1363-1395 ◽  
Author(s):  
Dror Aiger ◽  
Haim Kaplan ◽  
Micha Sharir
Keyword(s):  
Euclidean Space ◽  
High Dimensional ◽  
Dimensional Euclidean Space

ALGORITHMS FOR POINT SET MATCHING WITH k-DIFFERENCES

2006 ◽  
Vol 17 (04) ◽  
pp. 903-917
Author(s):  
TATSUYA AKUTSU
Keyword(s):  
Euclidean Space ◽  
Related Problem ◽  
Time Algorithm ◽  
Two Dimensions ◽  
Efficient Algorithms ◽  
Common Point ◽  
Dimensional Euclidean Space ◽  
Maximum Cardinality ◽  
Point Set ◽  
Special Case

The largest common point set problem (LCP) is, given two point set P and Q in d-dimensional Euclidean space, to find a subset of P with the maximum cardinality that is congruent to some subset of Q. We consider a special case of LCP in which the size of the largest common point set is at least (|P| + |Q| - k)/2. We develop efficient algorithms for this special case of LCP and a related problem. In particular, we present an O(k3n1.34 + kn2 log n) time algorithm for LCP in two-dimensions, which is much better for small k than an existing O(n3.2 log n) time algorithm, where n = max {|P|,|Q|}.

Results on the intersection of randomly located sets

1975 ◽  
Vol 12 (4) ◽  
pp. 817-823 ◽  
Author(s):  
Franz Streit
Keyword(s):  
Euclidean Space ◽  
Surface Area ◽  
Arbitrary Dimension ◽  
Expected Value ◽  
Dimensional Euclidean Space ◽  
Common Intersection ◽  
Point Set ◽  
The Common

Randomly generated subsets of a point-set A0 in the k-dimensional Euclidean space Rk are investigated. Under suitable restrictions the probability is determined that a randomly located set which hits A0. is a subset of A0. Some results on the expected value of the measure and the surface area of the common intersection-set formed by n randomly located objects and A0 are generalized and derived for arbitrary dimension k.

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