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Stabbing Pairwise Intersecting Disks by Five Points

University 8 Max Willert Institut für Informatik, Freie Universität Berlin , 14195 Berlin , Germany 9 Micha Sharir 10 Paul Seiferth 11 Liam Roditty Department of Computer Science, Bar Ilan University , Ramat ... - 434 , 1991 . Micha Sharir and Emo Welzl . A combinatorial bound for linear programming and related problems . Proc. 9th Sympos. Theoret. Aspects Comput. Sci. (STACS) , pages 567 - 579 , 1992 . Lajos

The Algebraic Revolution in Combinatorial and Computational Geometry: State of the Art (Invited Talk)

For the past 10 years, combinatorial geometry (and to some extent, computational geometry too) has gone through a dramatic revolution, due to the infusion of techniques from algebraic geometry and algebra that have proven effective in solving a variety of hard problems that were thought to be unreachable with more traditional techniques. The new era has begun with two...

Output Sensitive Algorithms for Approximate Incidences and Their Applications

German-Israeli Science Foundation and by Grant 1841-14 from the Israel Science Foundation. Work by Micha Sharir has been supported by Grant 2012/229 from the U.S.-Israel Binational Science Foundation, by

Finding Axis-Parallel Rectangles of Fixed Perimeter or Area Containing the Largest Number of Points

(center no. 4/11). Work by Micha Sharir has been supported by Grant 2012/229 from the U.S.-Israel Binational Science Foundation, by Grant 892/13 from the Israel Science Foundation, by the Israeli Centers

A Nearly Quadratic Bound for the Decision Tree Complexity of k-SUM

Structures, Geometrical Problems and Computations ? Work on this paper by Esther Ezra has been supported by NSF CAREER under grant CCF:AF 1553354. Work on this paper by Micha Sharir was supported by Grant 892

Incidences between Points and Lines in Three Dimensions

bound will continue to be worst-case tight by placing ? Work on this paper by Noam Solomon and Micha Sharir was supported by Grant 892/13 from the Israel Science Foundation. Work by Micha Sharir was also

The Number of Unit-Area Triangles in the Plane: Theme and Variations

the Israel Science Foundation and by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11). Work by Micha Sharir was also supported by Grant 2012/229 from the U.S.-Israel

Polynomials Vanishing on Cartesian Products: The Elekes-Szab\'o Theorem Revisited

, Elekes and R?nyai [1] proved the following result. Given a constant-degree real polynomial f (x, y), and finite sets A, B, C ? R each of size n, we have ? Work on this paper by Orit E. Raz and Micha Sharir ... was supported by Grant 892/13 from the Israel Science Foundation and by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11). Work by Micha Sharir was also supported by Grant

Polynomials Vanishing on Cartesian Products: The Elekes-Szab\'o Theorem Revisited

, Elekes and R?nyai [1] proved the following result. Given a constant-degree real polynomial f (x, y), and finite sets A, B, C ? R each of size n, we have ? Work on this paper by Orit E. Raz and Micha Sharir ... was supported by Grant 892/13 from the Israel Science Foundation and by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11). Work by Micha Sharir was also supported by Grant

Polynomials Vanishing on Cartesian Products: The Elekes-Szab\'o Theorem Revisited

, Elekes and R?nyai [1] proved the following result. Given a constant-degree real polynomial f (x, y), and finite sets A, B, C ? R each of size n, we have ? Work on this paper by Orit E. Raz and Micha Sharir ... was supported by Grant 892/13 from the Israel Science Foundation and by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11). Work by Micha Sharir was also supported by Grant

Range Minima Queries with Respect to a Random Permutation, and Approximate Range Counting

Foundation, and by Grant 975/06 from the Israel Science Fund (ISF). The work by Micha Sharir was partially supported by NSF Grants CCR-05-14079 and CCR-08-30272, by Grant 2006/194 from the U.S.-Israel

On Lines and Joints

Center for Geometry at Tel Aviv University. Work by Micha Sharir was also supported by NSF Grants CCF-05-14079 and CCF-08-30272, by Grant 155/05 from the Israel Science Fund. and by Grant 2006/194 from the

Polyhedral Voronoi Diagrams of Polyhedra in Three Dimensions

Computing). Work by Micha Sharir was also supported by NSF Grants CCR-97-32101 and CCR00-98246, by a grant from the U.S.-Israel Binational Science Foundation and by the Hermann MinkowskiMINERVA Center for

Points and triangles in the plane and halving planes in space

We prove that for any setS ofn points in the plane andn3−α triangles spanned by the points inS there exists a point (not necessarily inS) contained in at leastn3−3α/(c log5n) of the triangles. This implies that any set ofn points in three-dimensional space defines at most\(\sqrt[3]{{(c/2)}}n^{8/3} \log ^{5/3} n\) halving planes.

Lines Avoiding Unit Balls in Three Dimensions

and ITR CCR-00-81964. Work by Vladlen Koltun was also supported by NSF Grant CCR01-21555. Work by Micha Sharir was also supported by NSF Grants CCR-97-32101 and CCR-00-98246, by a grant from the Israeli

Efficient Algorithms for Maximum Regression Depth

We investigate algorithmic questions that arise in the statistical problem of computing lines or hyperplanes of maximum regression depth among a set of n points. We work primarily with a dual representation and find points of maximum undirected depth in an arrangement of lines or hyperplanes. An O(n d ) time and O(n d−1) space algorithm computes undirected depth of all points in...

Diameter, width, closest line pair, and parametric searching

supported by a grant from the U.S.-Israeli Binational ScienceFoundation. Work by Micha Sharir was also supported by ONR Grant N00014-90-J-1284,by NSF Grant CCR-89-01484,and by grants from the Fund for Basic

Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams

Discrete Comput Geom Daniel Leven 0 Micha Sharir 0 0 School of Mathematical Sciences, Tel Aviv University , Tel Aviv , Israel An O(n log n) algorithm for planning a purely translational motion for