2026-07-20T11:45:58Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7327 2024-03-06T10:40:05Z ddc:004 open_access

Path Queries on Functions Gagie, Travis He, Meng Navarro, Gonzalo succinct data structures integer functions range queries trees and permutations Let f : [1..n] -> [1..n] be a function, and l : [1..n] -> [1..s] indicate a label assigned to each element of the domain. We design several compact data structures that answer various queries on the labels of paths in f. For example, we can find the minimum label in f^k (i) for a given i and any k >= 0 in a given range [k1..k2], using n lg n + O(n) bits, or the minimum label in f^(-k) (i) for a given i and k > 0, using 2n lg n + O(n) bits, both in time O(lg n/ lg lg n). By using n lg s + o(n lg s) further bits, we can also count, within the same time, the number of elements within a range of labels, and report each such element in O(1 + lg s / lg lg n) additional time. Several other possible queries are considered, such as top-t queries and t-majorities. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Travis Gagie and Meng He and Gonzalo Navarro 2017 Is Part Of LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2017.5 urn:nbn:de:0030-drops-73274 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.5 eng https://creativecommons.org/licenses/by/3.0/legalcode