2026-08-17T12:46:03Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13255 2024-03-06T10:51:57Z ddc:004 open_access

String Indexing for Top-k Close Consecutive Occurrences Bille, Philip Gørtz, Inge Li Pedersen, Max Rishøj Rotenberg, Eva Steiner, Teresa Anna String indexing pattern matching consecutive occurrences The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string P, report all occurrences of P within S. In this paper, we study a basic and natural extension of string indexing called the string indexing for top-k close consecutive occurrences problem (Sitcco). Here, a consecutive occurrence is a pair (i,j), i < j, such that P occurs at positions i and j in S and there is no occurrence of P between i and j, and their distance is defined as j-i. Given a pattern P and a parameter k, the goal is to report the top-k consecutive occurrences of P in S of minimal distance. The challenge is to compactly represent S while supporting queries in time close to the length of P and k. We give two time-space trade-offs for the problem. Let n be the length of S, m the length of P, and ε ∈ (0,1]. Our first result achieves O(nlog n) space and optimal query time of O(m+k), and our second result achieves linear space and query time O(m+k^{1+ε}). Along the way, we develop several techniques of independent interest, including a new translation of the problem into a line segment intersection problem and a new recursive clustering technique for trees. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Philip Bille and Inge Li Gørtz and Max Rishøj Pedersen and Eva Rotenberg and Teresa Anna Steiner 2020 Is Part Of LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2020.14 urn:nbn:de:0030-drops-132558 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.14 eng https://creativecommons.org/licenses/by/3.0/legalcode