We propose a space-efficient data structure for orthogonal range search on suffix arrays. For general two-dimensional orthogonal range search problem on a set of n points, there exists an n log n (1+o(1))-bit data structure supporting O(log n)-time counting queries [Mäkinen, Navarro 2007]. The space matches the information-theoretic lower bound. However, if we focus on a point set representing a suffix array, there is a chance to obtain a space efficient data structure. We answer this question affirmatively. Namely, we propose a data structure for orthogonal range search on suffix arrays which uses O(1/(ε) n (H₀+1)) bits where H₀ is the order-0 entropy of the string and answers a counting query in O(n^ε) time for any constant ε>0. As an application, we give an O(1/(ε) n (H₀+1))-bit data structure for the range LCP problem.
@InProceedings{matsuda_et_al:LIPIcs.CPM.2020.23, author = {Matsuda, Kotaro and Sadakane, Kunihiko and Starikovskaya, Tatiana and Tateshita, Masakazu}, title = {{Compressed Orthogonal Search on Suffix Arrays with Applications to Range LCP}}, booktitle = {31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)}, pages = {23:1--23:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-149-8}, ISSN = {1868-8969}, year = {2020}, volume = {161}, editor = {G{\o}rtz, Inge Li and Weimann, Oren}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.23}, URN = {urn:nbn:de:0030-drops-121482}, doi = {10.4230/LIPIcs.CPM.2020.23}, annote = {Keywords: Orthogonal Range Search, Succinct Data Structure, Suffix Array} }
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