25 Search Results for "Nikolov, Aleksandar"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.39
Locality Sensitive Hashing in Hyperbolic Space

Authors: Chengyuan Deng, Jie Gao, Kevin Lu, Feng Luo, and Cheng Xin

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

Abstract
For a metric space (X, d), a family ℋ of locality sensitive hash functions is called (r, cr, p₁, p₂) sensitive if a randomly chosen function h ∈ ℋ has probability at least p₁ (at most p₂) to map any a, b ∈ X in the same hash bucket if d(a, b) ≤ r (or d(a, b) ≥ cr). Locality Sensitive Hashing (LSH) is one of the most popular techniques for approximate nearest-neighbor search in high-dimensional spaces, and has been studied extensively for Hamming, Euclidean, and spherical geometries. An (r, cr, p₁, p₂)-sensitive hash function enables approximate nearest neighbor search (i.e., returning a point within distance cr from a query q if there exists a point within distance r from q) with space O(n^{1+ρ}) and query time O(n^ρ) where ρ = (log 1/p₁)/(log 1/p₂). But LSH for hyperbolic spaces ℍ^d remains largely unexplored. In this work, we present the first LSH construction native to hyperbolic space. For the hyperbolic plane (d = 2), we show a construction achieving ρ ≤ 1/c, based on the hyperplane rounding scheme. For general hyperbolic spaces (d ≥ 3), we use dimension reduction from ℍ^d to ℍ² and the 2D hyperbolic LSH to get ρ ≤ 1.59/c. On the lower bound side, we show that the lower bound on ρ of Euclidean LSH extends to the hyperbolic setting via local isometry, therefore giving ρ ≥ 1/c².
Cite as

Chengyuan Deng, Jie Gao, Kevin Lu, Feng Luo, and Cheng Xin. Locality Sensitive Hashing in Hyperbolic Space. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{deng_et_al:LIPIcs.SoCG.2026.39,
  author =	{Deng, Chengyuan and Gao, Jie and Lu, Kevin and Luo, Feng and Xin, Cheng},
  title =	{{Locality Sensitive Hashing in Hyperbolic Space}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{39:1--39:19},
  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.2026.39},
  URN =		{urn:nbn:de:0030-drops-258454},
  doi =		{10.4230/LIPIcs.SoCG.2026.39},
  annote =	{Keywords: Locality Sensitive Hashing, Hyperbolic Geometry, Dimension Reduction, Approximate Nearest Neighbor Search}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.66
Fast Nearest Neighbor Search for 𝓁_p Metrics

Authors: Robert Krauthgamer and Nir Petruschka

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

Abstract
The Nearest Neighbor Search (NNS) problem asks to design a data structure that preprocesses an n-point dataset X lying in a metric space ℳ, so that given a query point q ∈ ℳ, one can quickly return a point of X minimizing the distance to q. The efficiency of such a data structure is evaluated primarily by the amount of space it uses and the time required to answer a query. We focus on the fast query-time regime, which is crucial for modern large-scale applications, where datasets are massive and queries must be processed online, and is often modeled by query time poly(d log n) when ℳ is a d-dimensional normed space. Our main result is such a randomized data structure for NNS in 𝓁_p^d spaces, p > 2, that achieves p^{O(1) + log log p} approximation with fast query time and poly(dn) space. Our data structure improves, or is incomparable to, the state-of-the-art for the fast query-time regime from [Bartal and Gottlieb, TCS 2019] and [Krauthgamer, Petruschka and Sapir, FOCS 2025].
Cite as

Robert Krauthgamer and Nir Petruschka. Fast Nearest Neighbor Search for 𝓁_p Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 66:1-66:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{krauthgamer_et_al:LIPIcs.SoCG.2026.66,
  author =	{Krauthgamer, Robert and Petruschka, Nir},
  title =	{{Fast Nearest Neighbor Search for 𝓁\underlinep Metrics}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{66:1--66:9},
  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.2026.66},
  URN =		{urn:nbn:de:0030-drops-258737},
  doi =		{10.4230/LIPIcs.SoCG.2026.66},
  annote =	{Keywords: Nearest neighbor search, metric embeddings, 𝓁\underlinep norm}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2025.2
Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk)

Authors: Monika Henzinger and Roodabeh Safavi

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

Abstract
We give an introduction into differential privacy in the dynamic setting, called the continual observation setting.
Cite as

Monika Henzinger and Roodabeh Safavi. Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk). In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.2,
  author =	{Henzinger, Monika and Safavi, Roodabeh},
  title =	{{Securing Dynamic Data: A Primer on Differentially Private Data Structures}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{2:1--2:14},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-244702},
  doi =		{10.4230/LIPIcs.ESA.2025.2},
  annote =	{Keywords: Differential privacy, continual observation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.27
Online Makespan Scheduling Under Scenarios

Authors: Ekin Ergen

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

Abstract
We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so that the maximum makespan under a scenario, i.e., the maximum makespan of any schedule restricted to a scenario, is minimized. For varying values of the number of scenarios and machines, we explore the competitiveness of online algorithms. We prove tight and near-tight bounds, several of which are achieved through novel constructions. In particular, we leverage the interplay between the unit processing time case of our problem and the hypergraph coloring problem both ways: We use hypergraph coloring techniques to steer an adversarial family of instances proving lower bounds for our problem, which in turn leads to lower bounds for several variants of online hypergraph coloring.
Cite as

Ekin Ergen. Online Makespan Scheduling Under Scenarios. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ergen:LIPIcs.ESA.2025.27,
  author =	{Ergen, Ekin},
  title =	{{Online Makespan Scheduling Under Scenarios}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{27:1--27:16},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-244950},
  doi =		{10.4230/LIPIcs.ESA.2025.27},
  annote =	{Keywords: online scheduling, scenario-based model, online algorithms}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.58
Equality Is Far Weaker Than Constant-Cost Communication

Authors: Mika Göös, Nathaniel Harms, and Artur Riazanov

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We exhibit an n-bit communication problem with a constant-cost randomized protocol but which requires n^Ω(1) deterministic (or even non-deterministic) queries to an Equality oracle. Therefore, even constant-cost randomized protocols cannot be efficiently "derandomized" using Equality oracles. This improves on several recent results and answers a question from the survey of Hatami and Hatami (SIGACT News 2024). It also gives a significantly simpler and quantitatively superior proof of the main result of Fang, Göös, Harms, and Hatami (STOC 2025), that constant-cost communication does not reduce to the k-Hamming Distance hierarchy.
Cite as

Mika Göös, Nathaniel Harms, and Artur Riazanov. Equality Is Far Weaker Than Constant-Cost Communication. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goos_et_al:LIPIcs.APPROX/RANDOM.2025.58,
  author =	{G\"{o}\"{o}s, Mika and Harms, Nathaniel and Riazanov, Artur},
  title =	{{Equality Is Far Weaker Than Constant-Cost Communication}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{58:1--58:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.58},
  URN =		{urn:nbn:de:0030-drops-244246},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.58},
  annote =	{Keywords: Equality oracle, constant-cost communication, gamma-2 norm, spectral norm}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.40
Sublinear Space Graph Algorithms in the Continual Release Model

Authors: Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Thus far, previously known edge-differentially private algorithms for most graph problems including densest subgraph and matchings in the continual release setting only output real-value estimates (not vertex subset solutions) and do not use sublinear space. Instead, they rely on computing exact graph statistics on the input [Hendrik Fichtenberger et al., 2021; Shuang Song et al., 2018]. In this paper, we leverage sparsification to address the above shortcomings for edge-insertion streams. Our edge-differentially private algorithms use sublinear space with respect to the number of edges in the graph while some also achieve sublinear space in the number of vertices in the graph. In addition, for the densest subgraph problem, we also output edge-differentially private vertex subset solutions; no previous graph algorithms in the continual release model output such subsets. We make novel use of assorted sparsification techniques from the non-private streaming and static graph algorithms literature to achieve new results in the sublinear space, continual release setting. This includes algorithms for densest subgraph, maximum matching, as well as the first continual release k-core decomposition algorithm. We also develop a novel sparse level data structure for k-core decomposition that may be of independent interest. To complement our insertion-only algorithms, we conclude with polynomial additive error lower bounds for edge-privacy in the fully dynamic setting, where only logarithmic lower bounds were previously known.
Cite as

Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou. Sublinear Space Graph Algorithms in the Continual Release Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 40:1-40:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{epasto_et_al:LIPIcs.APPROX/RANDOM.2025.40,
  author =	{Epasto, Alessandro and Liu, Quanquan C. and Mukherjee, Tamalika and Zhou, Felix},
  title =	{{Sublinear Space Graph Algorithms in the Continual Release Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{40:1--40:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.40},
  URN =		{urn:nbn:de:0030-drops-244064},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.40},
  annote =	{Keywords: Differential Privacy, Continual Release, Densest Subgraph, k-Core Decomposition, Maximum Matching}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.13
Quantum Speedup for Sampling Random Spanning Trees

Authors: Simon Apers, Minbo Gao, Zhengfeng Ji, and Chenghua Liu

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

Abstract
We present a quantum algorithm for sampling random spanning trees from a weighted graph in Õ(√{mn}) time, where n and m denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for dense graphs and achieves a quantum speedup over the best-known classical algorithm, which runs in Õ(m) time. The approach carefully combines, on one hand, a classical method based on "large-step" random walks for reduced mixing time and, on the other hand, quantum algorithmic techniques, including quantum graph sparsification and a sampling-without-replacement variant of Hamoudi’s multiple-state preparation. We also establish a matching lower bound, proving the optimality of our algorithm up to polylogarithmic factors. These results highlight the potential of quantum computing in accelerating fundamental graph sampling problems.
Cite as

Simon Apers, Minbo Gao, Zhengfeng Ji, and Chenghua Liu. Quantum Speedup for Sampling Random Spanning Trees. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{apers_et_al:LIPIcs.ICALP.2025.13,
  author =	{Apers, Simon and Gao, Minbo and Ji, Zhengfeng and Liu, Chenghua},
  title =	{{Quantum Speedup for Sampling Random Spanning Trees}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{13:1--13:21},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-233907},
  doi =		{10.4230/LIPIcs.ICALP.2025.13},
  annote =	{Keywords: Quantum Computing, Quantum Algorithms, Random Spanning Trees}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.66
Lipschitz Decompositions of Finite 𝓁_{p} Metrics

Authors: Robert Krauthgamer and Nir Petruschka

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

Abstract
Lipschitz decomposition is a useful tool in the design of efficient algorithms involving metric spaces. While many bounds are known for different families of finite metrics, the optimal parameters for n-point subsets of 𝓁_p, for p > 2, remained open, see e.g. [Naor, SODA 2017]. We make significant progress on this question and establish the bound β = O(log^{1-1/p} n). Building on prior work, we demonstrate applications of this result to two problems, high-dimensional geometric spanners and distance labeling schemes. In addition, we sharpen a related decomposition bound for 1 < p < 2, due to Filtser and Neiman [Algorithmica 2022].
Cite as

Robert Krauthgamer and Nir Petruschka. Lipschitz Decompositions of Finite 𝓁_{p} Metrics. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{krauthgamer_et_al:LIPIcs.SoCG.2025.66,
  author =	{Krauthgamer, Robert and Petruschka, Nir},
  title =	{{Lipschitz Decompositions of Finite 𝓁\underline\{p\} Metrics}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{66:1--66:14},
  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.2025.66},
  URN =		{urn:nbn:de:0030-drops-232182},
  doi =		{10.4230/LIPIcs.SoCG.2025.66},
  annote =	{Keywords: Lipschitz decompositions, metric embeddings, geometric spanners}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.6
String Problems in the Congested Clique Model

Authors: Shay Golan and Matan Kraus

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
In this paper we present algorithms for several string problems in the Congested Clique model. In the Congested Clique model, n nodes (computers) are used to solve some problem. The input to the problem is distributed among the nodes, and the communication between the nodes is conducted in rounds. In each round, every node is allowed to send an O(log n)-bit message to every other node in the network. We consider three fundamental string problems in the Congested Clique model. First, we present an O(1) rounds algorithm for string sorting that supports strings of arbitrary length. Second, we present an O(1) rounds combinatorial pattern matching algorithm. Finally, we present an O(log log n) rounds algorithm for the computation of the suffix array and the corresponding Longest Common Prefix array of a given string.
Cite as

Shay Golan and Matan Kraus. String Problems in the Congested Clique Model. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{golan_et_al:LIPIcs.CPM.2025.6,
  author =	{Golan, Shay and Kraus, Matan},
  title =	{{String Problems in the Congested Clique Model}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.6},
  URN =		{urn:nbn:de:0030-drops-231003},
  doi =		{10.4230/LIPIcs.CPM.2025.6},
  annote =	{Keywords: String Sorting, Pattern Matching, Suffix Array, Congested Clique, Sorting}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.15
Differentially Private High-Dimensional Approximate Range Counting, Revisited

Authors: Martin Aumüller, Fabrizio Boninsegna, and Francesco Silvestri

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Locality Sensitive Filters are known for offering a quasi-linear space data structure with rigorous guarantees for the Approximate Near Neighbor search (ANN) problem. Building on Locality Sensitive Filters, we derive a simple data structure for the Approximate Near Neighbor Counting (ANNC) problem under differential privacy (DP). Moreover, we provide a simple analysis leveraging a connection with concomitant statistics and extreme value theory. Our approach produces a simple data structure with a tunable parameter that regulates a trade-off between space-time and utility. Through this trade-off, our data structure achieves the same performance as the recent findings of Andoni et al. (NeurIPS 2023) while offering better utility at the cost of higher space and query time. In addition, we provide a more efficient algorithm under pure ε-DP and elucidate the connection between ANN and differentially private ANNC. As a side result, the paper provides a more compact description and analysis of Locality Sensitive Filters for Fair Near Neighbor Search, improving a previous result in Aumüller et al. (TODS 2022).
Cite as

Martin Aumüller, Fabrizio Boninsegna, and Francesco Silvestri. Differentially Private High-Dimensional Approximate Range Counting, Revisited. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 15:1-15:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aumuller_et_al:LIPIcs.FORC.2025.15,
  author =	{Aum\"{u}ller, Martin and Boninsegna, Fabrizio and Silvestri, Francesco},
  title =	{{Differentially Private High-Dimensional Approximate Range Counting, Revisited}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{15:1--15:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.15},
  URN =		{urn:nbn:de:0030-drops-231426},
  doi =		{10.4230/LIPIcs.FORC.2025.15},
  annote =	{Keywords: Differential Privacy, Locality Sensitive Filters, Approximate Range Counting, Concominant Statistics}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.3
Private Estimation When Data and Privacy Demands Are Correlated

Authors: Syomantak Chaudhuri and Thomas A. Courtade

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Differential Privacy (DP) is the current gold-standard for ensuring privacy for statistical queries. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We consider the problems of empirical mean estimation for univariate data and frequency estimation for categorical data, both subject to heterogeneous privacy constraints. Each user, contributing a sample to the dataset, is allowed to have a different privacy demand. The dataset itself is assumed to be worst-case and we study both problems under two different formulations - first, where privacy demands and data may be correlated, and second, where correlations are weakened by random permutation of the dataset. We establish theoretical performance guarantees for our proposed algorithms, under both PAC error and mean-squared error. These performance guarantees translate to minimax optimality in several instances, and experiments confirm superior performance of our algorithms over other baseline techniques.
Cite as

Syomantak Chaudhuri and Thomas A. Courtade. Private Estimation When Data and Privacy Demands Are Correlated. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chaudhuri_et_al:LIPIcs.FORC.2025.3,
  author =	{Chaudhuri, Syomantak and Courtade, Thomas A.},
  title =	{{Private Estimation When Data and Privacy Demands Are Correlated}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.3},
  URN =		{urn:nbn:de:0030-drops-231305},
  doi =		{10.4230/LIPIcs.FORC.2025.3},
  annote =	{Keywords: Differential Privacy, Personalized Privacy, Heterogeneous Privacy, Correlations in Privacy}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.8
Differential Privacy Under Multiple Selections

Authors: Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, and Sahasrajit Sarmasarkar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
We consider the setting where a user with sensitive features wishes to obtain a recommendation from a server in a differentially private fashion. We propose a "multi-selection" architecture where the server can send back multiple recommendations and the user chooses one from these that matches best with their private features. When the user feature is one-dimensional - on an infinite line - and the accuracy measure is defined w.r.t some increasing function 𝔥(.) of the distance on the line, we precisely characterize the optimal mechanism that satisfies differential privacy. The specification of the optimal mechanism includes both the distribution of the noise that the user adds to its private value, and the algorithm used by the server to determine the set of results to send back as a response. We show that Laplace is an optimal noise distribution in this setting. Furthermore, we show that this optimal mechanism results in an error that is inversely proportional to the number of results returned when the function 𝔥(.) is the identity function.
Cite as

Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, and Sahasrajit Sarmasarkar. Differential Privacy Under Multiple Selections. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 8:1-8:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goel_et_al:LIPIcs.FORC.2025.8,
  author =	{Goel, Ashish and Jiang, Zhihao and Korolova, Aleksandra and Munagala, Kamesh and Sarmasarkar, Sahasrajit},
  title =	{{Differential Privacy Under Multiple Selections}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{8:1--8:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.8},
  URN =		{urn:nbn:de:0030-drops-231353},
  doi =		{10.4230/LIPIcs.FORC.2025.8},
  annote =	{Keywords: Differential Privacy, Mechanism Design and Multi-Selection}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.6
Near-Universally-Optimal Differentially Private Minimum Spanning Trees

Authors: Richard Hladík and Jakub Tětek

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Devising mechanisms with good beyond-worst-case input-dependent performance has been an important focus of differential privacy, with techniques such as smooth sensitivity, propose-test-release, or inverse sensitivity mechanism being developed to achieve this goal. This makes it very natural to use the notion of universal optimality in differential privacy. Universal optimality is a strong instance-specific optimality guarantee for problems on weighted graphs, which roughly states that for any fixed underlying (unweighted) graph, the algorithm is optimal in the worst-case sense, with respect to the possible setting of the edge weights. In this paper, we give the first such result in differential privacy. Namely, we prove that a simple differentially private mechanism for approximately releasing the minimum spanning tree is near-optimal in the sense of universal optimality for the 𝓁₁ neighbor relation. Previously, it was only known that this mechanism is nearly optimal in the worst case. We then focus on the 𝓁_∞ neighbor relation, for which the described mechanism is not optimal. We show that one may implement the exponential mechanism for MST in polynomial time, and that this results in universal near-optimality for both the 𝓁₁ and the 𝓁_∞ neighbor relations.
Cite as

Richard Hladík and Jakub Tětek. Near-Universally-Optimal Differentially Private Minimum Spanning Trees. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hladik_et_al:LIPIcs.FORC.2025.6,
  author =	{Hlad{\'\i}k, Richard and T\v{e}tek, Jakub},
  title =	{{Near-Universally-Optimal Differentially Private Minimum Spanning Trees}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.6},
  URN =		{urn:nbn:de:0030-drops-231337},
  doi =		{10.4230/LIPIcs.FORC.2025.6},
  annote =	{Keywords: differential privacy, universal optimality, minimum spanning trees}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.7
O(1)-Round MPC Algorithms for Multi-Dimensional Grid Graph Connectivity, Euclidean MST and DBSCAN

Authors: Junhao Gan, Anthony Wirth, and Zhuo Zhang

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
In this paper, we investigate three fundamental problems in the Massively Parallel Computation (MPC) model: (i) grid graph connectivity, (ii) approximate Euclidean Minimum Spanning Tree (EMST), and (iii) approximate DBSCAN. Our first result is a O(1)-round Las Vegas (i.e., succeeding with high probability) MPC algorithm for computing the connected components on a d-dimensional c-penetration grid graph ((d,c)-grid graph), where both d and c are positive integer constants. In such a grid graph, each vertex is a point with integer coordinates in ℕ^d, and an edge can only exist between two distinct vertices with 𝓁_∞-norm at most c. To our knowledge, the current best existing result for computing the connected components (CC’s) on (d,c)-grid graphs in the MPC model is to run the state-of-the-art MPC CC algorithms that are designed for general graphs: they achieve O(log log n + log D) [Behnezhad et al., 2019] and O(log log n + log 1/(λ)) [Sepehr Assadi et al., 2019] rounds, respectively, where D is the diameter and λ is the spectral gap of the graph. With our grid graph connectivity technique, our second main result is a O(1)-round Las Vegas MPC algorithm for computing approximate Euclidean MST. The existing state-of-the-art result on this problem is the O(1)-round MPC algorithm proposed by Andoni et al. [Alexandr Andoni et al., 2014], which only guarantees an approximation on the overall weight in expectation. In contrast, our algorithm not only guarantees a deterministic overall weight approximation, but also achieves a deterministic edge-wise weight approximation. The latter property is crucial to many applications, such as finding the Bichromatic Closest Pair and Single-Linkage Clustering. Last, but not least, our third main result is a O(1)-round Las Vegas MPC algorithm for computing an approximate DBSCAN clustering in O(1)-dimensional Euclidean space.
Cite as

Junhao Gan, Anthony Wirth, and Zhuo Zhang. O(1)-Round MPC Algorithms for Multi-Dimensional Grid Graph Connectivity, Euclidean MST and DBSCAN. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gan_et_al:LIPIcs.ICDT.2025.7,
  author =	{Gan, Junhao and Wirth, Anthony and Zhang, Zhuo},
  title =	{{O(1)-Round MPC Algorithms for Multi-Dimensional Grid Graph Connectivity, Euclidean MST and DBSCAN}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.7},
  URN =		{urn:nbn:de:0030-drops-229483},
  doi =		{10.4230/LIPIcs.ICDT.2025.7},
  annote =	{Keywords: Massively Parallel Computation, Graph Connectivity, Grid Graphs, Euclidean Minimum Spanning Tree, DBSCAN}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.83
Fine-Grained Equivalence for Problems Related to Integer Linear Programming

Authors: Lars Rohwedder and Karol Węgrzycki

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Integer Linear Programming with n binary variables and m many 0/1-constraints can be solved in time 2^Õ(m²) poly(n) and it is open whether the dependence on m is optimal. Several seemingly unrelated problems, which include variants of Closest String, Discrepancy Minimization, Set Cover, and Set Packing, can be modelled as Integer Linear Programming with 0/1 constraints to obtain algorithms with the same running time for a natural parameter m in each of the problems. Our main result establishes through fine-grained reductions that these problems are equivalent, meaning that a 2^O(m^{2-ε}) poly(n) algorithm with ε > 0 for one of them implies such an algorithm for all of them. In the setting above, one can alternatively obtain an n^O(m) time algorithm for Integer Linear Programming using a straightforward dynamic programming approach, which can be more efficient if n is relatively small (e.g., subexponential in m). We show that this can be improved to {n'}^O(m) + O(nm), where n' is the number of distinct (i.e., non-symmetric) variables. This dominates both of the aforementioned running times.
Cite as

Lars Rohwedder and Karol Węgrzycki. Fine-Grained Equivalence for Problems Related to Integer Linear Programming. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 83:1-83:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder_et_al:LIPIcs.ITCS.2025.83,
  author =	{Rohwedder, Lars and W\k{e}grzycki, Karol},
  title =	{{Fine-Grained Equivalence for Problems Related to Integer Linear Programming}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{83:1--83:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.83},
  URN =		{urn:nbn:de:0030-drops-227114},
  doi =		{10.4230/LIPIcs.ITCS.2025.83},
  annote =	{Keywords: Integer Programming, Fine-Grained Complexity, Fixed-Parameter Tractable Algorithms}
}
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