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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
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
  • J. Pach, M. Sharir
  • Mathematics, Economics
    Combinatorics, Probability and Computing
  • 1 March 1998
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.
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.
Visibility Problems for Polyhedral Terrains
  • R. Cole, M. Sharir
  • Mathematics, Computer Science
    J. Symb. Comput.
  • 20 February 2018
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.