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

We present a simple randomized algorithm which solves linear programs withn constraints andd variables in expected time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise, the algorithm computes the lexicographically smallest nonnegative point satisfying linear inequalities ind variables.Expand

We present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within a triangulation of a simple polygonP.Expand

This paper continues the discussion, begun in J. Schwartz and M. Sharir [Comm. Pure Appl. Math., in press], of the following problem, which arises in robotics: Given a collection of bodies B, which… Expand

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

We review the recent progress in the design of efficient algorithms for various problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, ray shooting and other query-type problems.Expand

We show that a set of points in the plane determine O(n2 log n) triples that define the same angle α, and that for many angles α (including π 2 ) this bound is tight in the worst case.Expand