Since a real univariate polynomial does not always have real roots, a very natural
algorithmic problem, is to design a method to count the number of real roots of a given …

This book is primarily a textbook introduction to various areas of discrete geometry. In each
area, it explains several key results and methods, in an accessible and concrete manner. It …

Discrepancy theory is also called the theory of irregularities of distribution. Here are some
typical questions: What is the" most uniform" way of dis tributing n points in the unit square …

In this paper, a new algorithm for performing quantifier elimination from first order formulas
over real closed fields in given. This algorithm improves the complexity of the asymptotically …

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 …

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 & …

In this paper we give a new bound on the sum of the Betti numbers of semi-algebraic sets.
This extends a well-known bound due to Oleinik and Petrovsky [20], Thorn [25] and Milnor …

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 …

Data-driven workflows, of which IBM's Business Artifacts are a prime exponent, have been
successfully deployed in practice, adopted in industrial standards, and have spawned a rich …

We prove that every set system of bounded VC-dimension has a fractional Helly property.
More precisely, if the dual shatter function of a set system \FF is bounded by o(m^k), then \FF …