Binary space partitions for axis-parallel line segments: Size-height tradeoffs

Binary Space Partitions for Axis - Parallel Line Segments : Size - Height

We present worst-case lower bounds on the minimum size of a binary space partition (BSP) tree as a function of its height, for a set S of n axis-parallel line segments in the plane. We assume that the BSP uses only axis-parallel cutting lines. These lower bounds imply that, in the worst case, a BSP tree of height O(log n) must have size (n log n) and a BSP tree of size O(n) must have height (n)...

New Results on Binary Space Partitions in the Plane

We prove the existence of linear size binary space partitions for sets of objects in the plane under certain conditions. In particular, we construct linear size binary space partitions for sets of fat objects, for sets of line segments where the ratio between the lengths of the longest and shortest segment is bounded by a constant, and for homothetic objects. For all cases we also show how to t...

Binary Space Partitions: Recent Developments

A binary space partition tree is a data structure for the representation of a set of objects in space. It found an increasing number of applications over the last decades. In recent years, intensifying research focused on its combinatorial properties, which affect directly the efficiency of applications. Important advances were made on binary space partitions for disjoint line segments in the p...

Binary Spa e Partitions for Axis - Parallel Segments , Re tangles , and Hyperre tangles

Constructing Binary Space Partitions for Orthogonal Rectabgles in Practice

In this paper, we develop a simple technique for constructing a Binary Space Partition (BSP) for a set of orthogonal rectangles in R 3. Our algorithm has the novel feature that it tunes its performance to the geometric properties of the rectangles, e.g., their aspect ratios. We have implemented our algorithm and tested its performance on real data sets. We have also systematically compared the ...