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Documents authored by Pedersen, Max Rishøj

Document
DOI: 10.4230/LIPIcs.CPM.2023.4
Sliding Window String Indexing in Streams

Authors: Philip Bille, Johannes Fischer, Inge Li Gørtz, Max Rishøj Pedersen, and Tord Joakim Stordalen

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract
Given a string S over an alphabet Σ, the string indexing problem is to preprocess S to subsequently support efficient pattern matching queries, that is, given a pattern string P report all the occurrences of P in S. In this paper we study the streaming sliding window string indexing problem. Here the string S arrives as a stream, one character at a time, and the goal is to maintain an index of the last w characters, called the window, for a specified parameter w. At any point in time a pattern matching query for a pattern P may arrive, also streamed one character at a time, and all occurrences of P within the current window must be returned. The streaming sliding window string indexing problem naturally captures scenarios where we want to index the most recent data (i.e. the window) of a stream while supporting efficient pattern matching. Our main result is a simple O(w) space data structure that uses O(log w) time with high probability to process each character from both the input string S and any pattern string P. Reporting each occurrence of P uses additional constant time per reported occurrence. Compared to previous work in similar scenarios this result is the first to achieve an efficient worst-case time per character from the input stream with high probability. We also consider a delayed variant of the problem, where a query may be answered at any point within the next δ characters that arrive from either stream. We present an O(w + δ) space data structure for this problem that improves the above time bounds to O(log (w/δ)). In particular, for a delay of δ = ε w we obtain an O(w) space data structure with constant time processing per character. The key idea to achieve our result is a novel and simple hierarchical structure of suffix trees of independent interest, inspired by the classic log-structured merge trees.
Cite as

Philip Bille, Johannes Fischer, Inge Li Gørtz, Max Rishøj Pedersen, and Tord Joakim Stordalen. Sliding Window String Indexing in Streams. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bille_et_al:LIPIcs.CPM.2023.4,
  author =	{Bille, Philip and Fischer, Johannes and G{\o}rtz, Inge Li and Pedersen, Max Rish{\o}j and Stordalen, Tord Joakim},
  title =	{{Sliding Window String Indexing in Streams}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.4},
  URN =		{urn:nbn:de:0030-drops-179587},
  doi =		{10.4230/LIPIcs.CPM.2023.4},
  annote =	{Keywords: String indexing, pattern matching, sliding window, streaming}
}
Document
DOI: 10.4230/LIPIcs.CPM.2021.10
Gapped Indexing for Consecutive Occurrences

Authors: Philip Bille, Inge Li Gørtz, Max Rishøj Pedersen, and Teresa Anna Steiner

Published in: LIPIcs, Volume 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)

Abstract
The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting queries (return all positions where the pattern occurs), and counting queries (return the number of occurrences of the pattern). In this paper we consider a variant of string indexing, where the goal is to compactly represent the string such that given two patterns P₁ and P₂ and a gap range [α, β] we can quickly find the consecutive occurrences of P₁ and P₂ with distance in [α, β], i.e., pairs of subsequent occurrences with distance within the range. We present data structures that use Õ(n) space and query time Õ(|P₁|+|P₂|+n^{2/3}) for existence and counting and Õ(|P₁|+|P₂|+n^{2/3}occ^{1/3}) for reporting. We complement this with a conditional lower bound based on the set intersection problem showing that any solution using Õ(n) space must use Ω̃(|P₁| + |P₂| + √n) query time. To obtain our results we develop new techniques and ideas of independent interest including a new suffix tree decomposition and hardness of a variant of the set intersection problem.
Cite as

Philip Bille, Inge Li Gørtz, Max Rishøj Pedersen, and Teresa Anna Steiner. Gapped Indexing for Consecutive Occurrences. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bille_et_al:LIPIcs.CPM.2021.10,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Pedersen, Max Rish{\o}j and Steiner, Teresa Anna},
  title =	{{Gapped Indexing for Consecutive Occurrences}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.10},
  URN =		{urn:nbn:de:0030-drops-139615},
  doi =		{10.4230/LIPIcs.CPM.2021.10},
  annote =	{Keywords: String indexing, two patterns, consecutive occurrences, conditional lower bound}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.14
String Indexing for Top-k Close Consecutive Occurrences

Authors: Philip Bille, Inge Li Gørtz, Max Rishøj Pedersen, Eva Rotenberg, and Teresa Anna Steiner

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
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.
Cite as

Philip Bille, Inge Li Gørtz, Max Rishøj Pedersen, Eva Rotenberg, and Teresa Anna Steiner. String Indexing for Top-k Close Consecutive Occurrences. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bille_et_al:LIPIcs.FSTTCS.2020.14,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Pedersen, Max Rish{\o}j and Rotenberg, Eva and Steiner, Teresa Anna},
  title =	{{String Indexing for Top-k Close Consecutive Occurrences}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.14},
  URN =		{urn:nbn:de:0030-drops-132558},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.14},
  annote =	{Keywords: String indexing, pattern matching, consecutive occurrences}
}
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