Stabbing segments with rectilinear objects

Stabbing Segments with Rectilinear Objects

Given a set S of n line segments in the plane, we say that a region R ⊆ R is a stabber for S ifR contains exactly one endpoint of each segment of S. In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially different stabbers for several shapes of stabbers. Specifically, we consider the case in which the stabber can be described as the intersection of axis-pa...

Rectilinear Decompositions with Low Stabbing Number

On Rectilinear Partitions with Minimum Stabbing Number

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...

3 Stabbing segments

In this paper, we answer the question: Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection? We prove that already when the sets are segments in the plane, deciding existence of a convex stabber is NP-complete. On the positive side, we give a polynomial-time algorithm (in the full paper) to...

Computing Partitions of Rectilinear Polygons with Minimum Stabbing Number

The stabbing number of a partition of a rectilinear polygon P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment contained in P . We consider the problem of finding a rectangular partition with minimum stabbing number for a given rectilinear polygon P . First, we impose a conforming constraint on partitions: every vertex of every rectangle in the parti...