Visualization of glyphs has a long history in medical imaging but gains much more power when the glyphs are properly placed to fill the screen. Glyph packing is often performed via an iterative approach to improve the location of glyphs. We present an alternative implementation of glyph packing based on a Delaunay triangulation to speed up the clustering process and reduce costs for neighborhoo...

This paper proves a bottom-left placement theorem for the rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given rectangles into a rectangular container without overlapping, then we can achieve a feasible packing by successively placing a rectangle onto a bottom-left corner in the container. This theorem shows that even for the real-parameter rectang...

It is proved in [l] that if a tree T of order n is not a star, then there exists an edgedisjoint placement of two copies of this tree into its fourth power. In this paper, we prove the packing of some trees into their third power. @ 2003 Eisevier Ltd. Ali rights reserved. Keywords-Embedding, Packing, Permutation, Placement, Power tree.

We present a new approach to optimal rectangle packing, an NP-complete problem that can be used to model many simple scheduling tasks. Recent attempts at incorporating artificial intelligence search techniques to the problem of rectangle packing have focused on a CSP formulation, in which partial assignments are defined to be the fixed placement of a subset of rectangles. Our technique takes a ...

1-d bin packing and 2-d bin packing are classic NP-complete problems that are motivated by industrial applications of stock cutting, data storage, etc. In this paper, we look at a slightly more general problem that is primarily motivated by VLSI design. In VLSI design, one wants to pack a given number of rectangles (which might be RAM chips, transistors, etc.) into a wafer of minimum area to re...

We study two related problems in non-preemptive scheduling and packing of malleable tasks with precedence constraints to minimize the makespan. We distinguish the scheduling variant, in which we allow the free choice of processors, and the packing variant, in which a task must be assigned to a contiguous subset of processors. For precedence constraints of bounded width, we completely resolve th...

We present and contrast several efficient two-dimensional packing algorithms for specified aspect ratio. These near-linear algorithms are based on strip packing, tiling, and alternate-bisection methodologies and can be used in the layout of disconnected objects in graph visualization. The parameters that affect the performance of these algorithms as well as the circumstances under which they pe...

We present approximation algorithms for the twoand three-dimensional bin packing problems and the three-dimensional strip packing problem. We consider the special case of these problems in which a parameter (a positive integer) is given, indicating that each of the dimensions of the items to be packed is at most of the corresponding dimension of the recipient. We analyze the asymptotic performa...

This article shows some techniques based on simulated annealing and genetic alghoritms for the resolution of a filling problem of a container of two dimensions using rectangular pieces of sizes not congruent. This problem is quite related to problems like bin-packing or strip-packing. The comparative was made using several type problems and having into account parameters like run time, number o...