A central problem in computational geometry, range searching arises in many applications,
and numerous geometric problems can be formulated in terms of range searching. A typical …

A central problem in computational geometry, range searching arises in many applications,
and a variety of geometric problems can be formulated as range-searching problems. A …

An Incidence Theorem in Higher Dimensions | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Discrete & …

Arithmetic combinatorics is often concerned with the problem of controlling the possible
range of behaviours of arbitrary finite sets in a group or ring with respect to arithmetic …

Let P be a set of n points in R^d. We present a linear-size data structure for answering range
queries on P with constant-complexity semialgebraic sets as ranges, in time close to O(n^1 …

We show that m points and n two-dimensional algebraic surfaces in R^ 4 R 4 can have at
most O (m^ k/(2k-1) n^(2k-2)/(2k-1)+ m+ n) O (mk/(2 k-1) n (2 k-2)/(2 k-1)+ m+ n) incidences …

459 Polynomial partitioning for a set of varieties Page 1 Math. Proc. Camb. Phil. Soc. (2015),
159, 459–469 c Cambridge Philosophical Society 2015 doi:10.1017/S0305004115000468 …

In 2015, Guth proved that if S is a collection of n g-dimensional semialgebraic sets in R^d
and if D≧1 is an integer, then there is a d-variate polynomial P of degree at most D so that …

We show that $ m $ points and $ n $ smooth algebraic surfaces of bounded degree in $\RR^
3$ satisfying suitable nondegeneracy conditions can have at most $ O (m^{\frac {2k}{3k-1}} …

We show that a set of n algebraic plane curves of constant maximum degree can be cut into
O (n 3/2 polylog n) Jordan arcs, so that each pair of arcs intersect at most once, ie, they form …