Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Weak -nets and interval chains Noga Alon, Haim Kaplan, Gabriel Nivasch1
 

Summary: Weak -nets and interval chains
Noga Alon, Haim Kaplan, Gabriel Nivasch1
,
Micha Sharir, Shakhar Smorodinsky2
July 17, 2007
Abstract
We construct weak -nets of almost linear size for certain types of point sets.
Specifically, for planar point sets in convex position we construct weak 1
r -nets of
size O(r(r)), where (r) denotes the inverse Ackermann function. For point sets
along the moment curve in Rd
we construct weak 1
r -nets of size r 2poly((r))
, where
the degree of the polynomial in the exponent depends (quadratically) on d.
Our constructions result from a reduction to a new problem, which we call
stabbing interval chains with j-tuples. Given the range of integers N = [1, n], an
interval chain of length k is a sequence of k consecutive, disjoint, nonempty intervals
contained in N. A j-tuple p = (p1, . . . , pj) is said to stab an interval chain C =
I1 Ik if each pi falls on a different interval of C. The problem is to construct a

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics