Davenport Schinzel sequences are sequences that do not contain forbidden alternating
subsequences of certain length. They are a powerful combinatorial tool applicable in …

The arrangement of a finite collection of geometric objects is the decomposition of the space
into connected cells induced by them. We survey combinatorial and algorithmic properties of …

Given a finite collection S of geometric objects such as hyperplanes or spheres in Rd, the
arrangement A (S) is the decomposition of Rd into connected open cells of dimensions 0 …

We give a simple lazy randomized incremental algorithm to compute≤ k-levels in
arrangements of x-monotone Jordan curves in the plane, and in arrangements of planes in …

We re-examine the notion of relative (p, ε)-approximations, recently introduced in Cohen et
al.(Manuscript, 2006), and establish upper bounds on their size, in general range spaces of …

We describe general randomized reductions of certain geometric optimization problems to
their corresponding decision problems. These reductions increase the expected time …

Two novel applications of the plane sweep paradigm are demonstrated, namely, for the
computation of extended viewsheds on gridded DEMs and for class interval selection on TIN …

Given n points in three dimensions, we show how to answer halfspace range reporting
queries in O (log n+ k) expected time for an output size k. Our data structure can be …

We investigate the problem of finding the best solution satisfying all but k of the given
constraints, for an abstract class of optimization problems introduced by Sharir and Welzl …

Abstract An (n, s) Davenport–Schinzel sequence, for positive integers n and s, is a sequence
composed of n distinct symbols with the properties that no two adjacent elements are equal …