منابع مشابه
Packing the hypercube
Let G be a graph that is a subgraph of some n-dimensional hypercube Qn. For sufficiently large n, Stout [20] proved that it is possible to pack vertexdisjoint copies of G in Qn so that any proportion r < 1 of the vertices of Qn are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large n, it is possible to pack edge-disjoint copies of G in Qn so...
متن کاملImproved Online Hypercube Packing
In this paper, we study online multidimensional bin packing problem when all items are hypercubes. Based on the techniques in one dimensional bin packing algorithm Super Harmonic by Seiden, we give a framework for online hypercube packing problem and obtain new upper bounds of asymptotic competitive ratios. For square packing, we get an upper bound of 2.1439, which is better than 2.24437. For c...
متن کاملImproved Lower Bounds for Online Hypercube Packing
Packing a given sequence of items into as few bins as possible in an online fashion is a widely studied problem. We improve lower bounds for packing hypercubes into bins in two or more dimensions, once for general algorithms (in two dimensions) and once for an important subclass, so-called Harmonic-type algorithms (in two or more dimensions). Lastly, we show that two adaptions of the ideas from...
متن کاملBounds for online bounded space hypercube packing
In hypercube packing, we receive a sequence of hypercubes that need to be packed into unit hypercubes which are called bins. Items arrive online and each item must be placed within its bin without overlapping with other items in that bin. The goal is to minimize the total number of bins used. We present lower and upper bounds for online bounded space hypercube packing in dimensions 2,...,7. 200...
متن کاملDrawing lines by uniform packing
In this paper, we introduce a new approach to line drawing that attempts to maintain a uniform packing density of horizontal segments to diagonal segments throughout the line. While the conventional line drawing algorithms perform linear time computations to find the location of the pixels, our algorithm takes logarithmic time. Also, experimental results show that the quality of line is accepta...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90327-p