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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

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

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...

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

The complexity and construction of many faces in arrangements of lines and of segments

Illinois at Urbana-Champaign , Urbana, Ill 61801 , USA 2 Herbert Edelsbrunner , 1 Leonidas J. Guibas, 2'3 and Micha Sharir 4,s 3 5School of Mathematical Science , Tel AvivUniversity,69978Tel Aviv , Israel 4