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Documents authored by Svenning, Rolf

Document
DOI: 10.4230/LIPIcs.ESA.2025.5
External-Memory Priority Queues with Optimal Insertions

Authors: Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We present an external-memory priority queue structure supporting Insert and DeleteMin with amortized 𝒪(1) and 𝒪(lg N) comparisons, respectively, and amortized 𝒪(1/B) and 𝒪(1/B log_{M/B} N/B) I/Os, respectively. Here, M is the size of the internal memory, B is the block size of I/Os between internal and external memory, and N is the number of elements in the priority queue just before an operation is performed. Previous external-memory priority queues required amortized 𝒪(lg N) comparisons and 𝒪(1/B log_{M/B} N/B) I/Os for both Insert and DeleteMin. The construction requires the minimal assumption M ≥ 2B.
Cite as

Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning. External-Memory Priority Queues with Optimal Insertions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2025.5,
  author =	{Brodal, Gerth St{\o}lting and Goodrich, Michael T. and Iacono, John and Lo, Jared and Meyer, Ulrich and Pagan, Victor and Sitchinava, Nodari and Svenning, Rolf},
  title =	{{External-Memory Priority Queues with Optimal Insertions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.5},
  URN =		{urn:nbn:de:0030-drops-244734},
  doi =		{10.4230/LIPIcs.ESA.2025.5},
  annote =	{Keywords: priority queues, external memory, cache aware, amortized complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.82
Buffered Partially-Persistent External-Memory Search Trees

Authors: Gerth Stølting Brodal, Casper Moldrup Rysgaard, and Rolf Svenning

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We present an optimal partially-persistent external-memory search tree with amortized I/O bounds matching those achieved by the non-persistent B^{ε}-tree by Brodal and Fagerberg [SODA 2003]. In a partially-persistent data structure, each update creates a new version. All past versions can be queried, but only the current version can be updated. Operations should be efficient with respect to the size N_v of the accessed version v. For any parameter 0 < ε < 1, our data structure supports insertions and deletions in amortized 𝒪(1/(ε B^{1 - ε}) log_B N_v) I/Os, where B is the external-memory block size. It also supports successor and range reporting queries in amortized 𝒪(1/ε log_B N_v + K/B) I/Os, where K is the number of keys reported. The space usage of the data structure is linear in the total number of updates. We make the standard and minimal assumption that the internal memory has size M ≥ 2B. The previous state-of-the-art external-memory partially-persistent search tree by Arge, Danner and Teh [JEA 2003] supports all operations in worst-case 𝒪(log_B N_v + K/B) I/Os, matching the bounds achieved by the classical B-tree by Bayer and McCreight [Acta Informatica 1972]. Our data structure successfully combines buffering updates with partial persistence. The I/O bounds can also be achieved in the worst-case sense, by slightly modifying our data structure and under the requirement that the memory size M = Ω(B^{1-ε} log₂(max_v N_v)). For updates, where the I/O bound is o(1), we assume that the I/Os are performed evenly spread out among the updates (by performing buffer-overflows incrementally). The worst-case result slightly improves the memory requirement over the previous ephemeral external-memory dictionary by Das, Iacono, and Nekrich (ISAAC 2022), who achieved matching worst-case I/O bounds but required M = Ω(B log_B N), where N is the size of the current dictionary.
Cite as

Gerth Stølting Brodal, Casper Moldrup Rysgaard, and Rolf Svenning. Buffered Partially-Persistent External-Memory Search Trees. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 82:1-82:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2025.82,
  author =	{Brodal, Gerth St{\o}lting and Rysgaard, Casper Moldrup and Svenning, Rolf},
  title =	{{Buffered Partially-Persistent External-Memory Search Trees}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{82:1--82:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.82},
  URN =		{urn:nbn:de:0030-drops-245507},
  doi =		{10.4230/LIPIcs.ESA.2025.82},
  annote =	{Keywords: B-tree, buffered updates, partial persistence, external memory}
}
Artifact
Software
DOI: 10.4230/artifacts.23018
RolfSvenning/ContiguousArtGallery

Authors: Rolf Svenning

Abstract
Cite as

Rolf Svenning. RolfSvenning/ContiguousArtGallery (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{github_impl,
   title = {{RolfSvenning/ContiguousArtGallery}}, 
   author = {Svenning, Rolf},
   note = {Software, Independent Research Fund Denmark (DFF), grant 9131- 00113B, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:7cfaba2c09d953feb90a49f0e26370ea3f7719a7;origin=https://github.com/RolfSvenning/ContiguousArtGallery;visit=swh:1:snp:24512c962bdc05c9bff737a006e263acf6b13e78;anchor=swh:1:rev:af66971aa2b832e98dcd6b1fcf8eac88d5901b93}{\texttt{swh:1:dir:7cfaba2c09d953feb90a49f0e26370ea3f7719a7}} (visited on 2025-06-20)},
   url = {https://github.com/RolfSvenning/ContiguousArtGallery},
   doi = {10.4230/artifacts.23018},
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.20
Polynomial-Time Algorithms for Contiguous Art Gallery and Related Problems

Authors: Ahmad Biniaz, Anil Maheshwari, Magnus Christian Ring Merrild, Joseph S. B. Mitchell, Saeed Odak, Valentin Polishchuk, Eliot W. Robson, Casper Moldrup Rysgaard, Jens Kristian Refsgaard Schou, Thomas Shermer, Jack Spalding-Jamieson, Rolf Svenning, and Da Wei Zheng

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We introduce the contiguous art gallery problem which is to guard the boundary of a simple polygon with a minimum number of guards such that each guard covers exactly one contiguous portion of the boundary. Art gallery problems are often NP-hard. In particular, it is NP-hard to minimize the number of guards to see the boundary of a simple polygon, without the contiguity constraint. This paper is a merge of three concurrent works [Ahmad Biniaz et al., 2024; Magnus Christian Ring Merrild et al., 2024; Eliot W. Robson et al., 2024] each showing that (surprisingly) the contiguous art gallery problem is solvable in polynomial time. The common idea of all three approaches is developing a greedy function that maps a point on the boundary to the furthest point on the boundary so that the contiguous interval along the boundary between them could be guarded by one guard. Repeatedly applying this function immediately leads to an OPT+1 approximation. By studying this greedy algorithm, we present three different approaches that achieve an optimal solution. The first and second approach apply this greedy algorithm from different points on the boundary that could be found in advance or on the fly while traversing along the boundary (respectively). The third approach represents this function as a piecewise linear rational function, which can be reduced to an abstract arc cover problem involving infinite families of arcs. We identify other problems that can be represented by similar functions, and solve them via the third approach. From the combinatorial point of view, we show that any n-vertex polygon can be guarded by at most ⌊(n-2)/2⌋ guards. This bound is tight because there are polygons that require this many guards.
Cite as

Ahmad Biniaz, Anil Maheshwari, Magnus Christian Ring Merrild, Joseph S. B. Mitchell, Saeed Odak, Valentin Polishchuk, Eliot W. Robson, Casper Moldrup Rysgaard, Jens Kristian Refsgaard Schou, Thomas Shermer, Jack Spalding-Jamieson, Rolf Svenning, and Da Wei Zheng. Polynomial-Time Algorithms for Contiguous Art Gallery and Related Problems. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{biniaz_et_al:LIPIcs.SoCG.2025.20,
  author =	{Biniaz, Ahmad and Maheshwari, Anil and Merrild, Magnus Christian Ring and Mitchell, Joseph S. B. and Odak, Saeed and Polishchuk, Valentin and Robson, Eliot W. and Rysgaard, Casper Moldrup and Schou, Jens Kristian Refsgaard and Shermer, Thomas and Spalding-Jamieson, Jack and Svenning, Rolf and Zheng, Da Wei},
  title =	{{Polynomial-Time Algorithms for Contiguous Art Gallery and Related Problems}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.20},
  URN =		{urn:nbn:de:0030-drops-231720},
  doi =		{10.4230/LIPIcs.SoCG.2025.20},
  annote =	{Keywords: Art Gallery Problem, Computational Geometry, Combinatorics, Discrete Algorithms}
}
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