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Anchored Rectangle and Square Packings Balas, Kevin Dumitrescu, Adrian Tóth, Csaba Rectangle packing anchored rectangle greedy algorithm charging scheme approximation algorithm. For points p_1,...,p_n in the unit square [0,1]^2, an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles r_1,...,r_n in [0,1]^2 such that point p_i is a corner of the rectangle r_i (that is, r_i is anchored at p_i) for i=1,...,n. We show that for every set of n points in [0,1]^2, there is an anchored rectangle packing of area at least 7/12-O(1/n), and for every n, there are point sets for which the area of every anchored rectangle packing is at most 2/3. The maximum area of an anchored square packing is always at least 5/32 and sometimes at most 7/27. The above constructive lower bounds immediately yield constant-factor approximations, of 7/12 -epsilon for rectangles and 5/32 for squares, for computing anchored packings of maximum area in O(n log n) time. We prove that a simple greedy strategy achieves a 9/47-approximation for anchored square packings, and 1/3 for lower-left anchored square packings. Reductions to maximum weight independent set (MWIS) yield a QPTAS and a PTAS for anchored rectangle and square packings in n^{O(1/epsilon)} and exp(poly(log (n/epsilon))) time, respectively. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Kevin Balas and Adrian Dumitrescu and Csaba Tóth 2016 Is Part Of LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2016.13 urn:nbn:de:0030-drops-59054 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.13 eng https://creativecommons.org/licenses/by/3.0/legalcode