A close to linear bound on the maximum length of Davenport--Schinzel sequences enable us to derive sharp bounds on the combinatorial structure underlying various geometric problems, which in turn yields efficient algorithms for these problems.Expand

A simple randomized algorithm which solves linear programs withn constraints andd variables in expected time, and computes the lexicographically smallest nonnegative point satisfyingn given linear inequalities ind variables.Expand

Given a triangulation of a simple polygonP, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP. These problems include calculation… Expand

We apply an idea of Székely to prove a general upper bound on the number of incidences between a set of m points and a set of n ‘well-behaved’ curves in the plane.

A wide range of applications of parametric searching and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.Expand

A simple randomized algorithm which solves linear programs with n constraints and d variables in expected O(d32 d n) time, and holds for any input.Expand