133 search results - page 2 / 27 » On the distinct distances determined by a planar point set |
STOC
2003
ACM
14 years 5 months ago
2003
ACM
Improving an old result of Clarkson et al., we show that the number of distinct distances determined by a set P of n points in three-dimensional space is (n77/141) = (n0.546 ), fo...
COMPGEOM
2004
ACM
13 years 10 months ago
2004
ACM
Given a set P of n points in convex position in the plane, we prove that there exists a point p ∈ P such that the number of distinct distances from p is at least (13n−6)/36 . ...
ISAAC
2003
Springer
13 years 10 months ago
2003
Springer
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclid...
CORR
2002
Springer
13 years 4 months ago
2002
Springer
We introduce a new measure for planar point sets S that captures a combinatorial distance that S is from being a convex set: The reflexivity (S) of S is given by the smallest numb...
COMPGEOM
2004
ACM
13 years 10 months ago
2004
ACM
Let P be a set of n points in general position in the plane. Let Xk(P ) denote the number of empty convex k-gons determined by P. We derive, using elementary proof techniques, sev...