On R-trees with Low Stabbing Number
نویسندگان
چکیده
منابع مشابه
ar X iv : c s / 03 10 03 4 v 2 [ cs . C G ] 7 S ep 2 00 5 Minimizing the Stabbing Number of Matchings , Trees , and Triangulations ∗
The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the or...
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The stabbing number of a geometric structure in IR with respect to lines is the maximum number of times any line stabs (intersects) the structure. We present algorithms for constructing popular geometric data structures with small stabbing number and for computing lower bounds on an optimal solution. We evaluate our methods experimentally.
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Zuni´c. On the maximal number of edges of convex digital polygons included into a square grid. A simplex variant solving an m ×d linear program in O (min(m 2 , d 2)) expected number of pivot steps. A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension. 12 P. K. Agarwal. A deterministic algorithm for partitioning arrangements of lin...
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Let S be a set of n points in R, and let r be a parameter with 1 6 r 6 n. A rectilinear r-partition for S is a collection Ψ(S) := {(S1, b1), . . . , (St, bt)}, such that the sets Si form a partition of S, each bi is the bounding box of Si, and n/2r 6 |Si| 6 2n/r for all 1 6 i 6 t. The (rectilinear) stabbing number of Ψ(S) is the maximum number of bounding boxes in Ψ(S) that are intersected by a...
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