A method for computing the Disjoint-Sum-Of-Products (DSOP) form of Boolean functions is described. The algorithm exploits the property of the most binate variable in a set of cubes to compute a DSOP form. The technique uses a minimized Sum-Of-Products (SOP) cube list as input. Experimental results comparing the size of the DSOP cube list produced by this algorithm and those produced by other me...

Résumé. Une session d’analyse OLAP peut être définie comme une session interactive durant laquelle un utilisateur lance des requêtes pour naviguer dans un cube. Très souvent, choisir quelle partie du cube va être naviguée par la suite, et, de ce fait, concevoir la prochaine requête, est une tâche difficile. Dans cet article, nous proposons d’utiliser ce que tous les utilisateurs du système OLAP...

We consider the problem of embedding the n-dimensional cube into a rectangular grid with 2n vertices in such a way as to minimize the congestion, the maximum number of edges along any point of the grid. After presenting a short solution for the cutwidth problem of the n-cube (in which the n-cube is embedded into a path), we show how to extend the results to give an exact solution for the conges...

We study two variants of the problem of contact representation of planar graphs with axis-aligned boxes. In a cube-contact representation we realize each vertex with a cube, while in a proportional box-contact representation each vertex is an axis-aligned box with a prespecified volume. We present algorithms for constructing cube-contact representation and proportional box-contact representatio...

Polycube Ruby Implementation Cutting Plotter (Graphtec/CraftROBO) Folded Model PostScript Figure 8: The process by which paper origami can be constructed using the described algorithms. square was inserted as part of a row or column), and does not take into account any non-orthogonal creases made as a result of later steps. The PostScript file can be sent to a cutting plotter, which can etch th...

The vertex set of a halved cube Qd consists of a bipartition vertex set of a cube Qd and two vertices are adjacent if they have a common neighbour in the cube. Let d ≥ 5. Then it is proved that Qd is the only connected, ( d 2 ) -regular graph on 2d−1 vertices in which every edge lies in two d-cliques and two d-cliques do not intersect in a vertex.

In this brief contribution, we derive an exact expression for (n 1)-cube reliability in an n-cube using a new probability fault model and M existing random fault model. Approximate results are also obtained for m-cube reliability for values of m smaller than n I . We show that the proposed probability model for computing subcube reliability is equally accurate, but computationally more efficien...

In this paper, we propose a new notion of rep-cube which is a net of a cube, and it can be divided into some polygons such that each of them can be folded to a cube. This notion is inspired by polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infintely many distinct rep-cubes. We also extend t...

In this paper, we employ a novel approach to metarule-guided, multi-dimensional association rule mining which explores a data cube structure. We propose algorithms for metarule-guided mining: given a metarule containing p predicates, we compare mining on an n-dimensional (n-D) cube structure (where p < n) with mining on smaller multiple pdimensional cubes. In addition, we propose an efficient m...