53 Search Results for "Nekrich, Yakov"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.33
Visibility Queries in Simple Polygons

Authors: Sujoy Bhore, Chih-Hung Liu, Anurag Murty Naredla, Yakov Nekrich, Eunjin Oh, André van Renssen, Frank Staals, Haitao Wang, and Jie Xue

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
Given a simple polygon P with n vertices, we consider the problem of constructing a data structure for visibility queries: for any query point q ∈ P, compute the visibility polygon of q in P. To obtain O(log n + k) query time, where k is the size of the visibility polygon of q, the previous best result requires O(n³) space. In this paper, we propose a new data structure that uses O(n^{2+ε}) space, for any ε > 0, while achieving the same query time. If only O(n²) space is available, the best known result provides O(log² n + k) query time. We improve this to O(log n log log n + k) time. When restricted to o(n²) space, the only previously known approach, aside from the O(n)-time algorithm that computes the visibility polygon without preprocessing, is an O(n)-space data structure that supports O(k log n)-time queries. We construct a data structure using O(n log n) space that answers visibility queries in O(n^{1/2+ε} + k) time. In addition, for the special case in which q lies on the boundary of P, we build a data structure of O(n log n) space supporting O(log² n + k) query time; alternatively, we achieve O(log n + k) query time using O(n^{1+ε}) space. To achieve our results, we propose a new method for decomposing simple polygons, which may be of independent interest.
Cite as

Sujoy Bhore, Chih-Hung Liu, Anurag Murty Naredla, Yakov Nekrich, Eunjin Oh, André van Renssen, Frank Staals, Haitao Wang, and Jie Xue. Visibility Queries in Simple Polygons. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.ICALP.2026.33,
  author =	{Bhore, Sujoy and Liu, Chih-Hung and Naredla, Anurag Murty and Nekrich, Yakov and Oh, Eunjin and van Renssen, Andr\'{e} and Staals, Frank and Wang, Haitao and Xue, Jie},
  title =	{{Visibility Queries in Simple Polygons}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{33:1--33:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.33},
  URN =		{urn:nbn:de:0030-drops-264222},
  doi =		{10.4230/LIPIcs.ICALP.2026.33},
  annote =	{Keywords: simple polygons, visibility polygons, visibility queries, polygon decompositions}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.113
Incremental k-Lowest Planes and Planar k-Nearest Neighbor with Optimal Query Time

Authors: John Iacono, Yakov Nekrich, and Martin P. Seybold

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
In a set of planes in ℝ³, the k-lowest planes query asks for the k lowest planes pierced by a vertical line q. In this paper we describe a semi-dynamic insertion-only data structure that answers k-lowest planes queries in optimal O(log n+k) time. Our data structure uses O(n) space, where n is the number of stored planes, and supports insertions in O(log⁸ n) amortized time. This result provides the first query optimal data structures for several fundamental problems: - An insertion-only structure that answers 3D halfspace range reporting queries on a set of n points in O(log n+k) time, where k is the number of reported points. - An insertion-only structure that answers 3D vertical ray shooting queries on a set of n planes in O(log n+k) time, where k is the number of reported planes. - An insertion-only structure that answers planar k-nearest neighbor queries in O(log n + k) time for any prescribed k (specified at query time). - An insertion-only structure that answers planar circular range reporting queries in time O(log n + k), where k is the number of reported points. For all of the above problems the query bound O(log n + k) is optimal, even in the static scenario. All of the above structures use linear O(n) space and support insertions in O(log⁸ n) amortized time. We also obtain a query optimal static structure for a 4D problem. That is, one can compute in near-linear time a data structure that answers weighted halfspace range reporting queries in O(log n + k) time, where k is the number of reported points. The structure uses near-linear space.
Cite as

John Iacono, Yakov Nekrich, and Martin P. Seybold. Incremental k-Lowest Planes and Planar k-Nearest Neighbor with Optimal Query Time. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 113:1-113:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{iacono_et_al:LIPIcs.ICALP.2026.113,
  author =	{Iacono, John and Nekrich, Yakov and Seybold, Martin P.},
  title =	{{Incremental k-Lowest Planes and Planar k-Nearest Neighbor with Optimal Query Time}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{113:1--113:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.113},
  URN =		{urn:nbn:de:0030-drops-265027},
  doi =		{10.4230/LIPIcs.ICALP.2026.113},
  annote =	{Keywords: Data Structures, Dynamic Data Structures, k Nearest-Neighbor Queries}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.13
Practical Parallel Block Tree Construction

Authors: Robert Clausecker, Florian Kurpicz, and Etienne Palanga

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

Abstract
The block tree [Belazzougui et al., J. Comput. Syst. Sci. '21] is a compressed representation of a length-n text that supports access, rank, and select queries while requiring only O(z log n/z) words of space, where z is the number of Lempel-Ziv factors of the text. In other words, its space requirements are asymptotically comparable to those of the compressed text itself. In practice, block trees offer query performance comparable to that of state-of-the-art compressed rank and select indices. However, their construction is significantly slower, and the fastest known construction algorithms additionally require a significant amount of working memory. To address these limitations, we propose fast and lightweight parallel algorithms for the efficient construction of block trees. Our algorithm achieves similar construction speed than the currently fastest block tree construction algorithm on a single core and is up to eight times faster using 64 cores, while requiring an order of magnitude less memory. Overall, we achieve a speedup of up to 15.5 on 64 cores, which is in line with the parallel construction of the Lempel-Ziv compression.
Cite as

Robert Clausecker, Florian Kurpicz, and Etienne Palanga. Practical Parallel Block Tree Construction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clausecker_et_al:LIPIcs.SEA.2026.13,
  author =	{Clausecker, Robert and Kurpicz, Florian and Palanga, Etienne},
  title =	{{Practical Parallel Block Tree Construction}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{13:1--13:19},
  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.2026.13},
  URN =		{urn:nbn:de:0030-drops-260175},
  doi =		{10.4230/LIPIcs.SEA.2026.13},
  annote =	{Keywords: block tree, shared memory, compression, SIMD, Karp-Rabin fingerprints}
}
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.SEA.2026.11
Wavelet Forests Revisited

Authors: Eric Chiu and Dominik Kempa

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

Abstract
Rank and select queries are basic operations on sequences, with applications in compressed text indexes and other space-efficient data structures. One of the standard data structures supporting these queries is the wavelet tree. In this paper, we study wavelet forests, that is, wavelet-tree structures based on the fixed-block compression boosting technique. Such structures partition the input sequence into fixed-size blocks and build a separate wavelet tree for each block. Previous work showed that this approach yields strong practical performance for rank queries. We extend wavelet forests to support select queries. We show that select support can be added with little additional space overhead and that the resulting structures remain practically efficient. In experiments on a range of non-repetitive and repetitive inputs, wavelet forests are competitive with, and in most cases outperform, standalone wavelet-tree implementations. We also study the effect of internal parameters, including superblock size and navigational data, on select-query performance.
Cite as

Eric Chiu and Dominik Kempa. Wavelet Forests Revisited. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 11:1-11:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chiu_et_al:LIPIcs.SEA.2026.11,
  author =	{Chiu, Eric and Kempa, Dominik},
  title =	{{Wavelet Forests Revisited}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{11:1--11:11},
  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.2026.11},
  URN =		{urn:nbn:de:0030-drops-260152},
  doi =		{10.4230/LIPIcs.SEA.2026.11},
  annote =	{Keywords: wavelet tree, wavelet forest, select queries}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.2
Near-Real-Time Solutions for Online String Problems

Authors: Dominik Köppl and Gregory Kucherov

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
Based on the Breslauer-Italiano online suffix tree construction algorithm (2013) with double logarithmic worst-case guarantees on the update time per letter, we develop near-real-time algorithms for several classical problems on strings, including the computation of the longest repeating suffix array, the (reversed) Lempel-Ziv 77 factorization, and the maintenance of minimal unique substrings, all in an online manner. Our solutions improve over the best known running times for these problems in terms of the worst-case time per letter, for which we achieve a poly-log-logarithmic time complexity, within a linear space. Best known results for these problems require a poly-logarithmic time complexity per letter or only provide amortized complexity bounds. As a result of independent interest, we give conversions between the longest previous factor array and the longest repeating suffix array in space and time bounds based on their irreducible representations, which can have sizes sublinear in the length of the input string.
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Dominik Köppl and Gregory Kucherov. Near-Real-Time Solutions for Online String Problems. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.2,
  author =	{K\"{o}ppl, Dominik and Kucherov, Gregory},
  title =	{{Near-Real-Time Solutions for Online String Problems}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.2},
  URN =		{urn:nbn:de:0030-drops-259287},
  doi =		{10.4230/LIPIcs.CPM.2026.2},
  annote =	{Keywords: online algorithms, string algorithms, suffix tree, real-time computation, Lempel-Ziv factorization, minimal unique substrings}
}
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.2026.25
Compressed Index with Construction in Compressed Space

Authors: Dmitry Kosolobov

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
Suppose that we are given a string s of length n over an alphabet {0,1,…,n^O(1)} and δ is the string complexity of s, a known compression measure. We describe an index on s with O(δlog(n/δ)) space, measured in O(log n)-bit machine words, which can search in s any string of length m in O(m + (occ + 1)log^ε n) time, where occ is the number of occurrences and ε > 0 is any fixed constant (the big-O in the space bound hides factor 1/ε). Crucially, the index can be built in O(n log n) expected time by one left-to-right pass on the string s in a streaming fashion with O(δlog(n/δ)) construction space. The index does not use the Karp-Rabin fingerprints, and the randomization in the construction time can be eliminated by using deterministic dictionaries instead of hash tables (with a slowdown). The search time matches currently best results and the space is almost optimal (the known optimum is O(δlog n/(δα)), where α = log_σ n and σ is the alphabet size, and it coincides with O(δlog(n/δ)) when δ = O(n/α²)). This is the first index that can be constructed within such space and with such time guarantees. To avoid uninteresting marginal cases, all above bounds are stated for δ ≥ Ω(log log n).
Cite as

Dmitry Kosolobov. Compressed Index with Construction in Compressed Space. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 25:1-25:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kosolobov:LIPIcs.CPM.2026.25,
  author =	{Kosolobov, Dmitry},
  title =	{{Compressed Index with Construction in Compressed Space}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{25:1--25:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.25},
  URN =		{urn:nbn:de:0030-drops-259515},
  doi =		{10.4230/LIPIcs.CPM.2026.25},
  annote =	{Keywords: compressed index, pattern matching, string complexity, grammar, block tree}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.20
Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs

Authors: Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi

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

Abstract
A disk graph is the intersection graph of (closed) disks in the plane. We consider the classic problem of finding a maximum clique in a disk graph. For general disk graphs, the complexity of this problem is still open, but for unit disk graphs, it is well known to be in P. The currently fastest algorithm runs in time O(n^{7/3+ o(1)}), where n denotes the number of disks [Jared Espenant et al., 2023; J. Mark Keil and Debajyoti Mondal, 2025]. Moreover, for the case of disk graphs with t distinct radii, the problem has also recently been shown to be in XP. More specifically, it is solvable in time O^*(n^{2t}) [J. Mark Keil and Debajyoti Mondal, 2025]. In this paper, we present algorithms with improved running times by allowing for approximate solutions and by using randomization: [(i)] 1) for unit disk graphs, we give an algorithm that, with constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(n/ε²); and 2) for disk graphs with t distinct radii, we give a parameterized approximation scheme that, with a constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(f(t)⋅ (1/ε)^{O(t)} ⋅ n), for some (exponential) function f(t).
Cite as

Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi. Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gao_et_al:LIPIcs.SWAT.2026.20,
  author =	{Gao, Jie and Gawrychowski, Pawe{\l} and Giannopoulos, Panos and Mulzer, Wolfgang and Singh, Satyam and Staals, Frank and Zehavi, Meirav},
  title =	{{Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{20:1--20:17},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-260563},
  doi =		{10.4230/LIPIcs.SWAT.2026.20},
  annote =	{Keywords: Maximum Clique, Disk Graphs, Unit Disk Graphs, FPT Approximation}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.27
New Results on Three-Sided Skyline Range Counting and Reporting

Authors: Suruchi Kushwaha and Yakov Nekrich

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

Abstract
In the orthogonal skyline range counting (resp. reporting) problem we store the set of points P in a data structure so that for any query range Q the number of points (resp. the list of all points) on the skyline of Q∩ P can be found efficiently. In this paper we study two-dimensional range counting and reporting problems in the case when the query range is bounded on three sides. We describe a linear-space data structure that answers top-open three-sided skyline counting queries in O(log log N) time, where N is the number of points stored in the data structure. We also show that bottom-open three-sided skyline counting queries are as difficult as general four-sided queries and any data structure that uses O(Nlog^c N) space for a constant c requires Ω(log N/log log N) time to answer such queries. Next, we turn to skyline color range queries. In this variant of the problem each point in P is assigned a color and we must count (resp. report) the distinct colors of point on the skyline of Q∩ P. We describe an O(N)-space data structure that answers top-open three-sided color counting queries in O(log N/log log N) time. Finally, we study top-open three-sided skyline color reporting in the EM model and describe a data structure that uses linear space and answers queries in O(k/B+1) I/Os where k is the number of colors on the skyline. This is the first external-memory data structure with optimal query cost and space usage for this problem.
Cite as

Suruchi Kushwaha and Yakov Nekrich. New Results on Three-Sided Skyline Range Counting and Reporting. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kushwaha_et_al:LIPIcs.SWAT.2026.27,
  author =	{Kushwaha, Suruchi and Nekrich, Yakov},
  title =	{{New Results on Three-Sided Skyline Range Counting and Reporting}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{27:1--27:14},
  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.2026.27},
  URN =		{urn:nbn:de:0030-drops-260631},
  doi =		{10.4230/LIPIcs.SWAT.2026.27},
  annote =	{Keywords: Data Structures, Range Searching, Skyline Queries}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.81
Optimal-Cost Construction of Shallow Cuttings for 3-D Dominance Ranges in the I/O-Model

Authors: Yakov Nekrich and Saladi Rahul

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Shallow cuttings are a fundamental tool in computational geometry and spatial databases for solving offline and online range searching problems. For a set P of N points in 3-D, at SODA'14, Afshani and Tsakalidis designed an optimal O(N log₂N) time algorithm that constructs shallow cuttings for 3-D dominance ranges in internal memory. Even though shallow cuttings are used in the I/O-model to design space and query efficient range searching data structures, an efficient construction of them is not known till now. In this paper, we design an optimal-cost algorithm to construct shallow cuttings for 3-D dominance ranges. The number of I/Os performed by the algorithm is O (N/B log_{M/B}(N/B)), where B is the block size and M is the memory size. As two applications of the optimal-cost construction algorithm, we design fast algorithms for offline 3-D dominance reporting and offline 3-D approximate dominance counting. We believe that our algorithm will find further applications in offline 3-D range searching problems and in improving construction cost of data structures for 3-D range searching problems.
Cite as

Yakov Nekrich and Saladi Rahul. Optimal-Cost Construction of Shallow Cuttings for 3-D Dominance Ranges in the I/O-Model. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 81:1-81:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{nekrich_et_al:LIPIcs.SoCG.2026.81,
  author =	{Nekrich, Yakov and Rahul, Saladi},
  title =	{{Optimal-Cost Construction of Shallow Cuttings for 3-D Dominance Ranges in the I/O-Model}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{81:1--81:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.81},
  URN =		{urn:nbn:de:0030-drops-258884},
  doi =		{10.4230/LIPIcs.SoCG.2026.81},
  annote =	{Keywords: Data Structures, I/O-efficient algorithms, Orthogonal Range Searching}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.12
Dynamic and Streaming Algorithms for Union Volume Estimation

Authors: Sujoy Bhore, Karl Bringmann, Timothy M. Chan, and Yanheng Wang

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
The union volume estimation problem asks to (1±ε)-approximate the volume of the union of n given objects X₁,…,X_n ⊂ ℝ^d. In their seminal work in 1989, Karp, Luby, and Madras solved this problem in time O(n/ε²) in an oracle model where each object X_i can be accessed via three types of queries: obtain the volume of X_i, sample a random point from X_i, and test whether X_i contains a given point x. This running time was recently shown to be optimal [Bringmann, Larsen, Nusser, Rotenberg, and Wang, SoCG'25]. In another line of work, Meel, Vinodchandran, and Chakraborty [PODS'21] designed algorithms that read the objects in one pass using polylogarithmic time per object and polylogarithmic space; this can be phrased as a dynamic algorithm supporting insertions of objects for union volume estimation in the oracle model. In this paper, we study algorithms for union volume estimation in the oracle model that support both insertions and deletions of objects. We obtain the following results: 1) an algorithm supporting insertions and deletions in polylogarithmic update and query time and linear space (this is the first such dynamic algorithm, even for 2D triangles); 2) an algorithm supporting insertions and suffix queries (which generalizes the sliding window setting) in polylogarithmic update and query time and space; 3) an algorithm supporting insertions and deletions of convex bodies of constant dimension in polylogarithmic update and query time and space.
Cite as

Sujoy Bhore, Karl Bringmann, Timothy M. Chan, and Yanheng Wang. Dynamic and Streaming Algorithms for Union Volume Estimation. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.12,
  author =	{Bhore, Sujoy and Bringmann, Karl and Chan, Timothy M. and Wang, Yanheng},
  title =	{{Dynamic and Streaming Algorithms for Union Volume Estimation}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.12},
  URN =		{urn:nbn:de:0030-drops-258180},
  doi =		{10.4230/LIPIcs.SoCG.2026.12},
  annote =	{Keywords: union volume estimation, dynamic algorithms, streaming algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.87
Range Longest Increasing Subsequence and Its Relatives

Authors: Karthik C. S. and Saladi Rahul

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Longest increasing subsequence (LIS) is a classical textbook problem which is still actively studied in various computational models. In this work, we present a few results for the range longest increasing subsequence problem (Range-LIS) and its variants. The input to Range-LIS is a sequence 𝒮 of n real numbers and a collection 𝒬 of m query ranges and for each query in 𝒬, the goal is to report the LIS of the sequence 𝒮 restricted to that query. Our two main results are for the following generalizations of the Range-LIS problem: 2D Range Queries: In this variant of the Range-LIS problem, each query is a pair of ranges, one of indices and the other of values, and we provide a randomized algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k), where k is the cumulative length of the m output subsequences. This improves on the elementary Õ(mn) runtime algorithm when m = Ω(√n). Previously, the only known result breaking the quadratic barrier was of Tiskin [SODA'10] which could only handle 1D range queries (i.e., each query was a range of indices) and also just outputted the length of the LIS (instead of reporting the subsequence achieving that length). Subsequent to our paper, Gawrychowski, Gorbachev, and Kociumaka in a preprint have extended Tiskin’s approach to handle reporting 1D range queries in O(n(log n)³+m+k) time. Colored Sequences: In this variant of the Range-LIS problem, each element in 𝒮 is colored and for each query in 𝒬, the goal is to report a monochromatic LIS contained in the sequence 𝒮 restricted to that query. For 2D queries, we provide a randomized algorithm for this colored version with running time Õ(mn^{2/3}+ n^{5/3})+O(k). Moreover, for 1D queries, we provide an improved algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k). Thus, we again improve on the elementary Õ(mn) runtime algorithm. Additionally, we prove that assuming the well-known Combinatorial Boolean Matrix Multiplication Hypothesis, that the runtime for 1D queries is essentially tight for combinatorial algorithms. Our algorithms combine several tools such as dynamic programming (to precompute increasing subsequences with some desirable properties), geometric data structures (to efficiently compute the dynamic programming entries), random sampling (to capture elements which are part of the LIS), classification of query ranges into large LIS and small LIS, and classification of colors into light and heavy. We believe that our techniques will be of interest to tackle other variants of LIS problem and other range-searching problems.
Cite as

Karthik C. S. and Saladi Rahul. Range Longest Increasing Subsequence and Its Relatives. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 87:1-87:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karthikc.s._et_al:LIPIcs.ITCS.2026.87,
  author =	{Karthik C. S. and Rahul, Saladi},
  title =	{{Range Longest Increasing Subsequence and Its Relatives}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{87:1--87:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.87},
  URN =		{urn:nbn:de:0030-drops-253740},
  doi =		{10.4230/LIPIcs.ITCS.2026.87},
  annote =	{Keywords: Longest Increasing Subsequence, Range Query, Fine-Grained Complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.3
Circle-Segment Intersection Queries in Connected Geometric Graphs

Authors: Peyman Afshani, Yannick Bosch, and Sabine Storandt

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In this paper, we study the problem of efficiently reporting all intersections between a given set of line segments in the plane and a query circle, focusing on the case where the segments form the edges of a connected geometric graph. While previous data structures for circle-segment intersection queries on general segment sets incur high space or query time costs, we exploit the connectivity of the input to obtain significantly improved performance. In fact, we propose a new circle-segment intersection data structure that can be constructed in 𝒪((n + C) log³ n) time and space on connected graphs with n edges and C edge crossings. It answers intersection queries in 𝒪(k log³ n) time, where k denotes the output size. Our method relies on the construction of efficient circle-graph intersection oracles as well as a novel linear-time algorithm to partition the edges of the graph into balanced, connected components, which might be of independent interest. In a proof-of-concept experimental study on real-world road networks, we show that our novel data structure also performs well in practice. Even on networks with millions of edges, the construction time is within minutes and queries are answered in a few milliseconds.
Cite as

Peyman Afshani, Yannick Bosch, and Sabine Storandt. Circle-Segment Intersection Queries in Connected Geometric Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{afshani_et_al:LIPIcs.ISAAC.2025.3,
  author =	{Afshani, Peyman and Bosch, Yannick and Storandt, Sabine},
  title =	{{Circle-Segment Intersection Queries in Connected Geometric Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.3},
  URN =		{urn:nbn:de:0030-drops-249114},
  doi =		{10.4230/LIPIcs.ISAAC.2025.3},
  annote =	{Keywords: Intersection data structure, Graph partitioning, Dobkin-Kirkpatrick hierarchy}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.72
Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions

Authors: Noam Horowicz and Tsvi Kopelowitz

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

Abstract
In the snippets problem, the goal is to preprocess a text T so that given two pattern queries, P₁ and P₂, one can quickly locate the occurrences of the two patterns in T that are closest to each other, or report the distance between these occurrences. Kopelowitz and Krauthgamer [CPM2016] showed upper bound tradeoffs and conditional lower bounds tradeoffs for the snippets problem, by utilizing connections between the snippets problem and the problem of constructing a color distance oracle (CDO), which is a data structure that preprocess a set of points with associated colors so that given two colors c and c' one can quickly find the (distance between the) closest pair of points where one has color c and the other has color c'. However, the existing upper bound and lower bound curves are not tight. Inspired by recent advances by Kopelowitz and Vassilevska-Williams [ICALP2020] regarding tradeoff curves for Set-disjointness data structures, in this paper we introduce new conditionally optimal algorithms for a (1+ε) approximation version of the snippets problem and a (1+ε) approximation version of the CDO problem, by applying fast matrix multiplication. For example, for CDO on n points in an array, if the preprocessing time is Õ(n^a) and the query time is Õ(n^b) then, assuming that ω = 2 (where ω is the exponent of n in the runtime of the fastest matrix multiplication algorithm on two squared matrices of size n× n), we show that approximate CDO can be solved with the following tradeoff a + 2b = 2 (if 0 ≤ b ≤ 1/3) 2a + b = 3 (if 1/3 ≤ b ≤ 1). Moreover, we prove that for exact CDO on points in an array, the algorithm of Kopelowitz and Krauthgamer [CPM2016], which obtains a tradeoff of a+b = 2, is essentially optimal assuming that the strong all-pairs shortest paths hypothesis holds for randomized algorithms. Thus, we demonstrate that the exact version of CDO is strictly harder than the approximate version. Moreover, this separation carries over to the snippets problem.
Cite as

Noam Horowicz and Tsvi Kopelowitz. Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 72:1-72:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{horowicz_et_al:LIPIcs.ESA.2025.72,
  author =	{Horowicz, Noam and Kopelowitz, Tsvi},
  title =	{{Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{72:1--72:17},
  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.2025.72},
  URN =		{urn:nbn:de:0030-drops-245403},
  doi =		{10.4230/LIPIcs.ESA.2025.72},
  annote =	{Keywords: data structures, fast matrix multiplication, fine-grained complexity, pattern matching, distance oracles}
}
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