2026-07-22T11:19:20Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23119 2025-10-02T12:38:08Z ddc:004 open_access

Encodings for Range Minimum Queries over Bounded Alphabets Jo, Seungbum Satti, Srinivasa Rao Range minimum queries Encoding data structures Cartesian trees Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with arbitrary elements, there has not been any results developed for the case when the alphabet size is small, which is the case in many practical scenarios where RMQ structures are used. In this paper, we investigate the encoding complexity of RMQs on arrays over bounded alphabet. We consider both one-dimensional (1D) and two-dimensional (2D) arrays. For the 1D case, we present a near-optimal space encoding. For constant-sized alphabets, this also supports the queries in constant time. For the 2D case, we systematically analyze the 1-sided, 2-sided, 3-sided and 4-sided queries and derive lower bounds for encoding space, and also matching upper bounds that support efficient queries in most cases. Our results demonstrate that, even with the bounded alphabet restriction, the space requirements remain close to those for the general alphabet case. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Seungbum Jo and Srinivasa Rao Satti 2025 Is Part Of LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2025.25 urn:nbn:de:0030-drops-231198 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.25 eng https://creativecommons.org/licenses/by/4.0/legalcode