We consider various encodings that support range top-k queries on a two-dimensional array containing elements from a total order. For an m x n array, we first propose an almost optimal encoding for answering one-sided top-k queries, whose query range is restricted to [1 ... m][1 .. a], for 1 <= a <= n. Next, we propose an encoding for the general top-k queries that takes m^2 * lg(binom((k+1)n)(n)) + m * lg(m) + o(n) bits. This generalizes the one-dimensional top-k encoding of Gawrychowski and Nicholson [ICALP, 2015]. Finally, for a 2 x n array, we obtain a 2 lg(binom(3n)(n)) + 3n + o(n)-bit encoding for answering top-2 queries.
@InProceedings{jo_et_al:LIPIcs.CPM.2016.3, author = {Jo, Seungbum and Lingala, Rahul and Satti, Srinivasa Rao}, title = {{Encoding Two-Dimensional Range Top-k Queries}}, booktitle = {27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)}, pages = {3:1--3:11}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-012-5}, ISSN = {1868-8969}, year = {2016}, volume = {54}, editor = {Grossi, Roberto and Lewenstein, Moshe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.3}, URN = {urn:nbn:de:0030-drops-60704}, doi = {10.4230/LIPIcs.CPM.2016.3}, annote = {Keywords: Encoding model, top-k query, range minimum query} }
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