Rectilinear Binary Space Partitioning (BSP) trees are often used for solving various types of range searching problems including ray shooting. We propose a novel method for construction of rectilinear BSP trees for a preferred set of ray shooting queries. Particularly, we study ray sets formed by fixing either the direction or the origin of rays. We analyse and discuss the properties of constru...

In data sequences measured over space or time, an important problem is accurate detection of abrupt changes. partially labeled data, it to correctly predict presence/absence changes in positive/negative regions, both the train and test sets. One existing dynamic programming algorithm designed for prediction unlabeled regions (and ignores labels set); another fitting (but does not changepoints r...

We consider the problem of constructing of binary space partitions (BSP) for a set S of n hyperrectangles in arbitrary dimensional space. If the set S fulfills the low directional density condition defined in this paper then the resultant BSP has O(n) size and it can be constructed in O(n log n) time in R. The low directional density condition defines a new class of objects which we are able to...

We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (D1,D1)-partitionable planar graphs with respect to the property D1 ”to be a forest”.

Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some necessary and sufficient conditions. However, there exists one common trait among these conditions, that is they are established on the basis of all neighborho...

In this paper we tackle the problem of tetrahedralization by breaking non-convex polyhedra into convex subpolyhedra, tetrahedralizing these convex subpolyhedra and merging them together. We generate a Binary Space Partition (BSP) tree from the triangular faces of a polyhedron and use this to identify the convex subpolyhedra in the polyhedron. Each convex subpolyhedron is tetrahedralized individ...

In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of applications. The object of this paper is to extend that study in various ways. First, the relationship of partitions with no consecutive integers to a theorem of MacMahon and mock theta functions is explored independently. Secondly, we derive in a succinc...

This paper studies an extension of bi-semiorders in which a “frontier” is added between the various relations used. This extension is motivated by the study of additive representations of ordered partitions and coverings defined on product sets of two components.

Partitioning is a key issue within the Codesign process. As it usually consumes much time, it is important to make it as efficient as possible to avoid costly feedbacks. In this way, this paper describes a partitioning process based on a grouping technique intended to avoid high time overheads due to communications, as well as being able to work with a reliable estimation model.