2026-08-25T17:34:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27187 2026-08-25T13:18:17Z ddc:004 open_access

Near-Optimal and Efficient Encoding for Two-Dimensional Range Minimum Queries Gawrychowski, Paweł Górkiewicz, Adam Satti, Srinivasa Rao Encoding Range Minimum Queries Compact structure We consider the 2D RMQ encoding problem: given an m× n array of mn elements over a total order, encode it such that, for any query rectangle, the position of its maximum element can be reported without accessing the original array. For m ≤ n, it is known how to encode the array in 𝒪(mn min{m, log n}) bits with 𝒪(1)-time queries [Brodal et al., Algorithmica 2012], and also how to obtain an asymptotically optimal encoding consisting of 𝒪(mn log m) bits [Brodal et al., ESA 2013]. However, the latter approach does not prove any guarantee on the query time, and it appears to be inherently sequential: it requires scanning the whole encoding to answer a query. We design a different encoding that uses near-optimal space while allowing for efficient queries. More concretely, for every parameter κ ∈ [1, log log n], our encoding uses 𝒪(κ mn(log m + log log n)) bits and answers 2D RMQ queries in 𝒪(log^{1/κ} n) time. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Paweł Gawrychowski and Adam Górkiewicz and Srinivasa Rao Satti 2026 Is Part Of LIPIcs, Volume 388, 34th Annual European Symposium on Algorithms (ESA 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2026.51 urn:nbn:de:0030-drops-271874 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.51 eng https://creativecommons.org/licenses/by/4.0/legalcode