Efficient 1-Space Bounded Hypercube Packing Algorithm
نویسندگان
چکیده
منابع مشابه
Bounds 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...
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In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional sp...
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We analyze approximation algorithms for bounded-space bin packing by comparing them against the optimal bounded-space packing (instead of comparing them against the globally optimal packing that does not necessarily satisfy the bounded-space constraint). For 2-boundedspace bin packing we construct a polynomial time offline approximation algorithm with asymptotic worst case ratio 3/2, and we sho...
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In this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items) arrive one by one, each item must be packed into a square bin of unit size on its arrival without any information about future items. When packing items, 90◦-rotation is allowed. 1-space bounded means there is only one “active” bin. If the “active” bin cannot acco...
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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...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2020
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-020-00723-5