6 Search Results for "Houen, Jakob Bæk Tejs"

Document
DOI: 10.4230/LIPIcs.SEA.2026.19
Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction

Authors: Vojtěch Gaďurek and Pavel Veselý

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

Abstract
Invertible Bloom Lookup Tables (IBLTs) provide a highly space-efficient way to reconstruct small sets resulting from a large number of insertions and deletions of elements, such as in streaming or distributed computation of the symmetric difference of similar sets. The set recovery process succeeds if the IBLT size is at least 1.22 times the size of the encoded set; otherwise, a 2-core occurs with high probability in the corresponding random hypergraph. However, the sets in practice often exhibit structure that allows for performance beyond worst-case bounds. Here, we demonstrate that structured sets - such as the k-mers in the symmetric difference of two closely related genomes - can be recovered with an IBLT of significantly smaller size. We achieve this by employing structure-aware predictors to break the 2-core whenever the recovery process gets stuck. Importantly, this approach modifies only the decoding procedure, leaving the IBLT data structure unchanged. We prove that even a weak matching-based predictor enables the recovery of 27% more elements than the nominal IBLT size. Equipped with simple predictors for k-mers of genomic datasets, we demonstrate that recovering a symmetric difference with high probability can be done with an IBLT of size only 66% of the encoded set size for k = 31, improving the space efficiency by almost a factor of two. Moreover, we design an improved method for k-mers with large k that combines subsampling with nearly perfect prediction via fingerprinting and achieves a scaling property, requiring only O(M log M) bits for recovering M k-mers, instead of Θ(k⋅M) bits of the standard IBLT. Overall, our results highlight the possibility of significant space-efficiency improvements for IBLTs on datasets with predictable structure.
Cite as

Vojtěch Gaďurek and Pavel Veselý. Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gadurek_et_al:LIPIcs.SEA.2026.19,
  author =	{Ga\v{d}urek, Vojt\v{e}ch and Vesel\'{y}, Pavel},
  title =	{{Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{19:1--19:24},
  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.2026.19},
  URN =		{urn:nbn:de:0030-drops-260237},
  doi =		{10.4230/LIPIcs.SEA.2026.19},
  annote =	{Keywords: Invertible Bloom Lookup Table, symmetric difference, k-mer sets}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.117
Incremental Approximate Single-Source Shortest Paths with Predictions

Authors: Samuel McCauley, Benjamin Moseley, Aidin Niaparast, Helia Niaparast, and Shikha Singh

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The algorithms-with-predictions framework has been used extensively to develop online algorithms with improved beyond-worst-case competitive ratios. Recently, there is growing interest in leveraging predictions for designing data structures with improved beyond-worst-case running times. In this paper, we study the fundamental data structure problem of maintaining approximate shortest paths in incremental graphs in the algorithms-with-predictions model. Given a sequence σ of edges that are inserted one at a time, the goal is to maintain approximate shortest paths from the source to each vertex in the graph at each time step. Before any edges arrive, the data structure is given a prediction of the online edge sequence σ̂ which is used to "warm start" its state. As our main result, we design a learned algorithm that maintains (1+ε)-approximate single-source shortest paths, which runs in Õ(m η log W/ε) time, where W is the weight of the heaviest edge and η is the prediction error. We show these techniques immediately extend to the all-pairs shortest-path setting as well. Our algorithms are consistent (performing nearly as fast as the offline algorithm) when predictions are nearly perfect, have a smooth degradation in performance with respect to the prediction error and, in the worst case, match the best offline algorithm up to logarithmic factors. That is, the algorithms are "ideal" in the algorithms-with-predictions model. As a building block, we study the offline incremental approximate single-source shortest-path (SSSP) problem. In the offline incremental SSSP problem, the edge sequence σ is known a priori and the goal is to construct a data structure that can efficiently return the length of the shortest paths in the intermediate graph G_t consisting of the first t edges, for all t. Note that the offline incremental problem is defined in the worst-case setting (without predictions) and is of independent interest.
Cite as

Samuel McCauley, Benjamin Moseley, Aidin Niaparast, Helia Niaparast, and Shikha Singh. Incremental Approximate Single-Source Shortest Paths with Predictions. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 117:1-117:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mccauley_et_al:LIPIcs.ICALP.2025.117,
  author =	{McCauley, Samuel and Moseley, Benjamin and Niaparast, Aidin and Niaparast, Helia and Singh, Shikha},
  title =	{{Incremental Approximate Single-Source Shortest Paths with Predictions}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{117:1--117:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.117},
  URN =		{urn:nbn:de:0030-drops-234946},
  doi =		{10.4230/LIPIcs.ICALP.2025.117},
  annote =	{Keywords: Algorithms with Predictions, Shortest Paths, Approximation Algorithms, Dynamic Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.9
Daisy Bloom Filters

Authors: Ioana O. Bercea, Jakob Bæk Tejs Houen, and Rasmus Pagh

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
A filter is a widely used data structure for storing an approximation of a given set S of elements from some universe 𝒰 (a countable set). It represents a superset S' ⊇ S that is "close to S" in the sense that for x ∉ S, the probability that x ∈ S' is bounded by some ε > 0. The advantage of using a Bloom filter, when some false positives are acceptable, is that the space usage becomes smaller than what is required to store S exactly. Though filters are well-understood from a worst-case perspective, it is clear that state-of-the-art constructions may not be close to optimal for particular distributions of data and queries. Suppose, for instance, that some elements are in S with probability close to 1. Then it would make sense to always include them in S', saving space by not having to represent these elements in the filter. Questions like this have been raised in the context of Weighted Bloom filters (Bruck, Gao and Jiang, ISIT 2006) and Bloom filter implementations that make use of access to learned components (Vaidya, Knorr, Mitzenmacher, and Krask, ICLR 2021). In this paper, we present a lower bound for the expected space that such a filter requires. We also show that the lower bound is asymptotically tight by exhibiting a filter construction that executes queries and insertions in worst-case constant time, and has a false positive rate at most ε with high probability over input sets drawn from a product distribution. We also present a Bloom filter alternative, which we call the Daisy Bloom filter, that executes operations faster and uses significantly less space than the standard Bloom filter.
Cite as

Ioana O. Bercea, Jakob Bæk Tejs Houen, and Rasmus Pagh. Daisy Bloom Filters. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bercea_et_al:LIPIcs.SWAT.2024.9,
  author =	{Bercea, Ioana O. and Houen, Jakob B{\ae}k Tejs and Pagh, Rasmus},
  title =	{{Daisy Bloom Filters}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.9},
  URN =		{urn:nbn:de:0030-drops-200491},
  doi =		{10.4230/LIPIcs.SWAT.2024.9},
  annote =	{Keywords: Bloom filters, input distribution, learned data structures}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.62
Bias Reduction for Sum Estimation

Authors: Talya Eden, Jakob Bæk Tejs Houen, Shyam Narayanan, Will Rosenbaum, and Jakub Tětek

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
In classical statistics and distribution testing, it is often assumed that elements can be sampled exactly from some distribution 𝒫, and that when an element x is sampled, the probability 𝒫(x) of sampling x is also known. In this setting, recent work in distribution testing has shown that many algorithms are robust in the sense that they still produce correct output if the elements are drawn from any distribution 𝒬 that is sufficiently close to 𝒫. This phenomenon raises interesting questions: under what conditions is a "noisy" distribution 𝒬 sufficient, and what is the algorithmic cost of coping with this noise? In this paper, we investigate these questions for the problem of estimating the sum of a multiset of N real values x_1, …, x_N. This problem is well-studied in the statistical literature in the case 𝒫 = 𝒬, where the Hansen-Hurwitz estimator [Annals of Mathematical Statistics, 1943] is frequently used. We assume that for some (known) distribution 𝒫, values are sampled from a distribution 𝒬 that is pointwise close to 𝒫. That is, there is a parameter γ < 1 such that for all x_i, (1 - γ) 𝒫(i) ≤ 𝒬(i) ≤ (1 + γ) 𝒫(i). For every positive integer k we define an estimator ζ_k for μ = ∑_i x_i whose bias is proportional to γ^k (where our ζ₁ reduces to the classical Hansen-Hurwitz estimator). As a special case, we show that if 𝒬 is pointwise γ-close to uniform and all x_i ∈ {0, 1}, for any ε > 0, we can estimate μ to within additive error ε N using m = Θ(N^{1-1/k}/ε^{2/k}) samples, where k = ⌈lg ε/lg γ⌉. We then show that this sample complexity is essentially optimal. Interestingly, our upper and lower bounds show that the sample complexity need not vary uniformly with the desired error parameter ε: for some values of ε, perturbations in its value have no asymptotic effect on the sample complexity, while for other values, any decrease in its value results in an asymptotically larger sample complexity.
Cite as

Talya Eden, Jakob Bæk Tejs Houen, Shyam Narayanan, Will Rosenbaum, and Jakub Tětek. Bias Reduction for Sum Estimation. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 62:1-62:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{eden_et_al:LIPIcs.APPROX/RANDOM.2023.62,
  author =	{Eden, Talya and Houen, Jakob B{\ae}k Tejs and Narayanan, Shyam and Rosenbaum, Will and T\v{e}tek, Jakub},
  title =	{{Bias Reduction for Sum Estimation}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{62:1--62:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.62},
  URN =		{urn:nbn:de:0030-drops-188872},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.62},
  annote =	{Keywords: bias reduction, sum estimation, sublinear time algorithms, sample complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.76
A Sparse Johnson-Lindenstrauss Transform Using Fast Hashing

Authors: Jakob Bæk Tejs Houen and Mikkel Thorup

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
The Sparse Johnson-Lindenstrauss Transform of Kane and Nelson (SODA 2012) provides a linear dimensionality-reducing map A ∈ ℝ^{m × u} in 𝓁₂ that preserves distances up to distortion of 1 + ε with probability 1 - δ, where m = O(ε^{-2} log 1/δ) and each column of A has O(ε m) non-zero entries. The previous analyses of the Sparse Johnson-Lindenstrauss Transform all assumed access to a Ω(log 1/δ)-wise independent hash function. The main contribution of this paper is a more general analysis of the Sparse Johnson-Lindenstrauss Transform with less assumptions on the hash function. We also show that the Mixed Tabulation hash function of Dahlgaard, Knudsen, Rotenberg, and Thorup (FOCS 2015) satisfies the conditions of our analysis, thus giving us the first analysis of a Sparse Johnson-Lindenstrauss Transform that works with a practical hash function.
Cite as

Jakob Bæk Tejs Houen and Mikkel Thorup. A Sparse Johnson-Lindenstrauss Transform Using Fast Hashing. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 76:1-76:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{houen_et_al:LIPIcs.ICALP.2023.76,
  author =	{Houen, Jakob B{\ae}k Tejs and Thorup, Mikkel},
  title =	{{A Sparse Johnson-Lindenstrauss Transform Using Fast Hashing}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{76:1--76:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.76},
  URN =		{urn:nbn:de:0030-drops-181281},
  doi =		{10.4230/LIPIcs.ICALP.2023.76},
  annote =	{Keywords: dimensionality reduction, hashing, concentration bounds, moment bounds}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.74
Understanding the Moments of Tabulation Hashing via Chaoses

Authors: Jakob Bæk Tejs Houen and Mikkel Thorup

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Simple tabulation hashing dates back to Zobrist in 1970 and is defined as follows: Each key is viewed as c characters from some alphabet Σ, we have c fully random hash functions h₀, …, h_{c - 1} : Σ → {{0, …, 2^l - 1}}, and a key x = (x₀, …, x_{c - 1}) is hashed to h(x) = h₀(x₀) ⊕ … ⊕ h_{c - 1}(x_{c - 1}) where ⊕ is the bitwise XOR operation. The previous results on tabulation hashing by Pǎtraşcu and Thorup [J.ACM'11] and by Aamand et al. [STOC'20] focused on proving Chernoff-style tail bounds on hash-based sums, e.g., the number keys hashing to a given value, for simple tabulation hashing, but their bounds do not cover the entire tail. Thus their results cannot bound moments. The paper Dahlgaard et al. [FOCS'15] provides a bound on the moments of certain hash-based sums, but their bound only holds for constant moments, and we need logarithmic moments. Chaoses are random variables of the form ∑ a_{i₀, …, i_{c - 1}} X_{i₀} ⋅ … ⋅ X_{i_{c - 1}} where X_i are independent random variables. Chaoses are a well-studied concept from probability theory, and tight analysis has been proven in several instances, e.g., when the independent random variables are standard Gaussian variables and when the independent random variables have logarithmically convex tails. We notice that hash-based sums of simple tabulation hashing can be seen as a sum of chaoses that are not independent. This motivates us to use techniques from the theory of chaoses to analyze hash-based sums of simple tabulation hashing. In this paper, we obtain bounds for all the moments of hash-based sums for simple tabulation hashing which are tight up to constants depending only on c. In contrast with the previous attempts, our approach will mostly be analytical and does not employ intricate combinatorial arguments. The improved analysis of simple tabulation hashing allows us to obtain bounds for the moments of hash-based sums for the mixed tabulation hashing introduced by Dahlgaard et al. [FOCS'15]. With simple tabulation hashing, there are certain inputs for which the concentration is much worse than with fully random hashing. However, with mixed tabulation, we get logarithmic moment bounds that are only a constant factor worse than those with fully random hashing for any possible input. This is a strong addition to other powerful probabilistic properties of mixed tabulation hashing proved by Dahlgaard et al.
Cite as

Jakob Bæk Tejs Houen and Mikkel Thorup. Understanding the Moments of Tabulation Hashing via Chaoses. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 74:1-74:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{houen_et_al:LIPIcs.ICALP.2022.74,
  author =	{Houen, Jakob B{\ae}k Tejs and Thorup, Mikkel},
  title =	{{Understanding the Moments of Tabulation Hashing via Chaoses}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{74:1--74:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.74},
  URN =		{urn:nbn:de:0030-drops-164154},
  doi =		{10.4230/LIPIcs.ICALP.2022.74},
  annote =	{Keywords: hashing, concentration bounds, moment bounds}
}
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