Improved Lower Bounds for Online Hypercube and Rectangle Packing

July 05, 2016 Β· Declared Dead Β· πŸ› arXiv.org

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Authors David Blitz, Sandy Heydrich, Rob van Stee, AndrΓ© van Vliet, Gerhard J. Woeginger arXiv ID 1607.01229 Category cs.DS: Data Structures & Algorithms Citations 3 Venue arXiv.org Last Checked 4 months ago
Abstract
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 boxes into bins in two or more dimensions, both for general algorithms for squares and rectangles (in two dimensions) and for an important subclass, so-called Harmonic-type algorithms for hypercubes (in two or more dimensions). Lastly, we show that two adaptions of ideas from a one-dimensional packing algorithm to square packing do not help to break the barrier of 2.
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