• Publications
  • Influence
Davenport-Schinzel sequences and their geometric applications
TLDR
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
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A subexponential bound for linear programming
TLDR
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
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Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons
TLDR
We present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within a triangulation of a simple polygonP. Expand
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Filling gaps in the boundary of a polyhedron
TLDR
In this paper we present an algorithm for detecting and repairing defects in the boundary of a polyhedron. Expand
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On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
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, whichExpand
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On the Number of Incidences Between Points and Curves
  • J. Pach, M. Sharir
  • Mathematics, Computer Science
  • Comb. Probab. Comput.
  • 1 March 1998
TLDR
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
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Combinatorial complexity bounds for arrangements of curves and spheres
TLDR
We present upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike. Expand
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Efficient algorithms for geometric optimization
TLDR
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
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Visibility Problems for Polyhedral Terrains
TLDR
In this paper we study several problems concerning the visibility of a polyhedral terrain @s from a point (or several points) lying above it. Expand
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Repeated Angles in the Plane and Related Problems
TLDR
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
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