4 Search Results for "Skjoldjensen, Frederik Rye"

Document
DOI: 10.4230/LIPIcs.SEA.2026.7
From Relative Compression to Hierarchical Compression

Authors: Philip Bille, Inge Li Gørtz, and Máximo Pérez-López

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
We introduce a framework to use any relative compression algorithm as a subroutine for hierarchical relative compression. In a dataset consisting of n sequences, it consists of constructing a rooted tree on the sequences, using hashing and similarity techniques, and compressing the children of a node relative to their parent. We build up on previous techniques [Bille et al., 2023], and optimize them further for computational efficiency. We test our framework with three existing relative compression algorithms on six genomic datasets, and we show that in datasets that contain heterogeneous data, hierarchical relative compression improves the compression ratio by a factor 2 or more, when compared to relative compression to a single sequence. Apart from compression ratio, we also explore the trade-offs with respect to compression speed, dataset decompression speed, and average sequence decompression speed. With two of the surveyed algorithms, dataset decompression becomes faster and sequence decompression remains practical, at the cost of compression time, which remains competitive for the datasets with highest variability.
Cite as

Philip Bille, Inge Li Gørtz, and Máximo Pérez-López. From Relative Compression to Hierarchical Compression. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bille_et_al:LIPIcs.SEA.2026.7,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{From Relative Compression to Hierarchical Compression}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.7},
  URN =		{urn:nbn:de:0030-drops-260117},
  doi =		{10.4230/LIPIcs.SEA.2026.7},
  annote =	{Keywords: Relative compression, RLZ, string collections, compressed representation, data structures, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.13
Faster Algorithms for Shortest Unique or Absent Substrings

Authors: Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) in a string S of length n. Both problems admit folklore 𝒪(n)-time solutions using the suffix tree of S. However, for small alphabets, this complexity is not necessarily optimal in the word RAM model, where a string of length n over alphabet [0,σ) can be stored in 𝒪(n log σ/log n) space and read in 𝒪(n log σ/log n) time. We present an 𝒪(n log σ/√{log n})-time algorithm for computing a SUS in S. This algorithm decomposes the problem according to the length and the period of the sought substring and uses several tools and techniques, such as synchronizing sets, the analysis of runs, and wavelet trees, to reduce the computation of a SUS to a simple geometric problem. Further, we adapt this algorithm and combine it with an efficient construction of de Bruijn sequences in order to obtain an 𝒪(n log σ/√{log n})-time algorithm for computing a SAS in S.
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba. Faster Algorithms for Shortest Unique or Absent Substrings. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.SWAT.2026.13,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Pissis, Solon P. and Verbeek, Hilde and Zuba, Wiktor},
  title =	{{Faster Algorithms for Shortest Unique or Absent Substrings}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.13},
  URN =		{urn:nbn:de:0030-drops-260493},
  doi =		{10.4230/LIPIcs.SWAT.2026.13},
  annote =	{Keywords: string algorithms, unique substrings, absent substrings, absent words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2017.6
Deterministic Indexing for Packed Strings

Authors: Philip Bille, Inge Li Gørtz, and Frederik Rye Skjoldjensen

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)

Abstract
Given a string S of length n, the classic string indexing problem is to preprocess S into a compact data structure that supports efficient subsequent pattern queries. In the deterministic variant the goal is to solve the string indexing problem without any randomization (at preprocessing time or query time). In the packed variant the strings are stored with several character in a single word, giving us the opportunity to read multiple characters simultaneously. Our main result is a new string index in the deterministic and packed setting. Given a packed string S of length n over an alphabet s, we show how to preprocess S in O(n) (deterministic) time and space O(n) such that given a packed pattern string of length m we can support queries in (deterministic) time O(m/a + log m + log log s), where a = w /log s is the number of characters packed in a word of size w = log n. Our query time is always at least as good as the previous best known bounds and whenever several characters are packed in a word, i.e., log s << w, the query times are faster.
Cite as

Philip Bille, Inge Li Gørtz, and Frederik Rye Skjoldjensen. Deterministic Indexing for Packed Strings. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 6:1-6:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bille_et_al:LIPIcs.CPM.2017.6,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Skjoldjensen, Frederik Rye},
  title =	{{Deterministic Indexing for Packed Strings}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{6:1--6:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.6},
  URN =		{urn:nbn:de:0030-drops-73351},
  doi =		{10.4230/LIPIcs.CPM.2017.6},
  annote =	{Keywords: suffix tree, suffix array, deterministic algorithm, word packing}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.18
Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation

Authors: Philip Bille, Patrick Hagge Cording, Inge Li Gørtz, Frederik Rye Skjoldjensen, Hjalte Wedel Vildhøj, and Søren Vind

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
Given a static reference string R and a source string S, a relative compression of S with respect to R is an encoding of S as a sequence of references to substrings of R. Relative compression schemes are a classic model of compression and have recently proved very successful for compressing highly-repetitive massive data sets such as genomes and web-data. We initiate the study of relative compression in a dynamic setting where the compressed source string S is subject to edit operations. The goal is to maintain the compressed representation compactly, while supporting edits and allowing efficient random access to the (uncompressed) source string. We present new data structures that achieve optimal time for updates and queries while using space linear in the size of the optimal relative compression, for nearly all combinations of parameters. We also present solutions for restricted and extended sets of updates. To achieve these results, we revisit the dynamic partial sums problem and the substring concatenation problem. We present new optimal or near optimal bounds for these problems. Plugging in our new results we also immediately obtain new bounds for the string indexing for patterns with wildcards problem and the dynamic text and static pattern matching problem.
Cite as

Philip Bille, Patrick Hagge Cording, Inge Li Gørtz, Frederik Rye Skjoldjensen, Hjalte Wedel Vildhøj, and Søren Vind. Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bille_et_al:LIPIcs.ISAAC.2016.18,
  author =	{Bille, Philip and Cording, Patrick Hagge and G{\o}rtz, Inge Li and Skjoldjensen, Frederik Rye and Vildh{\o}j, Hjalte Wedel and Vind, S{\o}ren},
  title =	{{Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.18},
  URN =		{urn:nbn:de:0030-drops-67872},
  doi =		{10.4230/LIPIcs.ISAAC.2016.18},
  annote =	{Keywords: Relative compression, dynamic compression, dynamic partial sum, sub-string concatenation, external macro compression}
}
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