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Davenport-Schinzel sequences and their geometric applications
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.
A subexponential bound for linear programming
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.
Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons
- L. Guibas, J. Hershberger, D. Leven, M. Sharir, R. Tarjan
- Computer Science, MathematicsAlgorithmica
- 1 March 1987
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…
On the Number of Incidences Between Points and Curves
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.
On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
Filling gaps in the boundary of a polyhedron
Efficient algorithms for geometric optimization
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.
Repeated Angles in the Plane and Related Problems
Visibility Problems for Polyhedral Terrains
A Combinatorial Bound for Linear Programming and Related Problems
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.