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An (n; s) Davenport{Schinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly non-contiguous) subsequence, any alternation a b a b of length s + 2 between two distinct symbols a and b. The close relationship between… (More)

- Jirí Matousek, Micha Sharir, Emo Welzl
- Algorithmica
- 1992

We present a simple randomized algorithm which solves linear programs with <italic>n</italic> constraints and <italic>d</italic> variables in expected <italic>O</italic>(<italic>nde</italic><supscrpt>(<italic>d</italic> ln(<italic>n</italic>+1))<supscrpt>1/4</supscrpt></supscrpt>) time in the unit cost model (where we count the number of arithmetic… (More)

- Sergiu Hart, Micha Sharir
- FOCS
- 1984

Davenport-Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in the computation of the envelope of a set of functions. We show that the maximal length of a Davenport-Schinzel sequence composed of n symbols is 6(noc(n»), where t1.(n)is the functional inverse of Ackermann's function, and is thus very… (More)

- Bud Mishra, Jacob T. Schwartz, Micha Sharir
- Algorithmica
- 1987

We study the criteria under which an object can be gripped by a multifingered dexterous hand, assuming no static friction between the object and the fingers; such grips are calledpositive grips. We study three cases in detail: (i) the body is at equilibrium, (ii) the body is under some constant external force/torque, and (iii) the body is under a varying… (More)

- Micha Sharir, Emo Welzl
- STACS
- 1992

- Leonidas J. Guibas, John Hershberger, Daniel Leven, Micha Sharir, Robert E. Tarjan
- Algorithmica
- 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 of the collection of all shortest paths insideP from a given source vertexS to all the other vertices ofP, calculation of the subpolygon ofP consisting of… (More)

- Micha Sharir, Emo Welzl
- SIAM J. Comput.
- 2006

We show that a set of <i>n</i> points in the plane has at most <i>O</i>(10.05<sup><i>n</i></sup>) perfect matchings with crossing-free straight-line embedding. The expected number of perfect crossing-free matchings of a set of <i>n</i> points drawn i.i.d. from an arbitrary distribution in the plane is at most <i>O</i>(9.24<sup><i>n</i></sup>).Several… (More)

- Sariel Har-Peled, Micha Sharir
- Discrete & Computational Geometry
- 2011

We reexamine the notion of relative (p, ε)-approximations, recently introduced in [CKMS06], and establish upper bounds on their size, in general range spaces of finite VC-dimension, using the sampling theory developed in [LLS01] and in several earlier studies [Pol86, Hau92, Tal94]. We also survey the different notions of sampling, used in computational… (More)

- Leonidas J. Guibas, Donald E. Knuth, Micha Sharir
- Algorithmica
- 1990

In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more “on-line” than earlier similar methods, takes expected timeO(nℝgn) and spaceO(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and… (More)

- Micha Sharir, Amir Schorr
- SIAM J. Comput.
- 1984

We consider the problem of computing the shortest path between two points in two- or three-dimensional space bounded by polyhedral surfaces. In the 2-D case the problem is easily solved in time <italic>O</italic>(<italic>n</italic><supscrpt>2</supscrpt> log <italic>n</italic>).In the general 3-D case the problem is quite hard to solve, and is not even… (More)