43 Search Results for "Cohen, Ilan"


Document
Exploring the Gap Between LCS and LCStr

Authors: Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom

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


Abstract
The Longest Common Subsequence (LCS) problem and the Longest Common Substring (LCStr) problem are classical string problems with broad theoretical and practical significance. The former has a quadratic conditional lower bound [FOCS, 2015], while the latter admits a linear-time solution. In this paper, we study a natural variation of these problems, the Longest Common Subsequence-Substring (LCSS) problem. The LCSS problem seeks the longest string that is simultaneously a subsequence of one input string and a substring of the other. This variant bridges LCS and LCStr, raising intriguing algorithmic questions: Does the complexity of computing LCSS interpolate between the linear time of LCStr and the quadratic time of LCS? What about approximability? We also examine a natural extension of LCSS to multiple strings, parameterizing the balance between subsequence and substring requirements. Our results reveal several insights. First, under the SETH conjecture, the inherent complexity of LCSS is quadratic, similar to LCS. In contrast, we provide a linear-time approximation for LCSS. Finally, for the multi-string variant, unlike both problems, we design a quadratic-time algorithm, uncovering deeper structural properties of the problem. By studying the complexity of the LCSS problem, we aim to gain some understanding of what influences whether a variant of the LCS problem behaves more like the standard LCS or like LCStr. Our findings suggest that hybrid constraints can create computational "sweet spots," where problems become more tractable than their pure counterparts. This opens a broader research direction in constraint-mediated algorithm design. Beyond LCSS itself, our work highlights unexpected connections between subsequence and substring constraints, advancing the theoretical understanding of string problems and laying the foundation for new algorithmic techniques and complexity-theoretic insights in the rich space between classical string comparison paradigms.

Cite as

Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom. Exploring the Gap Between LCS and LCStr. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{golan_et_al:LIPIcs.CPM.2026.27,
  author =	{Golan, Shay and Kraus, Matan and Porat, Ely and Shalom, B. Riva},
  title =	{{Exploring the Gap Between LCS and LCStr}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{27:1--27:21},
  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.2026.27},
  URN =		{urn:nbn:de:0030-drops-259535},
  doi =		{10.4230/LIPIcs.CPM.2026.27},
  annote =	{Keywords: Longest Common Subsequence, Longest Common Substring, Conditional Lower Bound}
}
Document
A Differentially Private Approximation of the Width Problem

Authors: Mor Hale and Or Sheffet

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)


Abstract
The width of a point set - the minimum distance between two parallel hyperplanes enclosing the data - is a fundamental geometric measure that captures how "flat" or "fat" a dataset is. As such, it serves as a basic shape descriptor used in visualization, convex hull approximation, and geometric data analysis. Despite its importance, width is highly sensitive to single-point changes, and no differentially private algorithm for approximating it was previously known. We present the first pure ε-differentially private algorithm that approximates the width of a dataset. Our algorithm is a private adaptation of Chan’s approximation scheme [Chan, 2000] and operates by privately approximating the solution to a collection of suitably formulated linear programs. In addition to estimating the width, our method privately identifies a corresponding direction, enabling a private "fattening" transformation of the dataset - a basic structural preprocessing step for many geometric algorithms. This work advances the understanding of how geometric shape descriptors can admit good approximations even under the constraints of differential privacy.

Cite as

Mor Hale and Or Sheffet. A Differentially Private Approximation of the Width Problem. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{hale_et_al:LIPIcs.FORC.2026.18,
  author =	{Hale, Mor and Sheffet, Or},
  title =	{{A Differentially Private Approximation of the Width Problem}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.18},
  URN =		{urn:nbn:de:0030-drops-259914},
  doi =		{10.4230/LIPIcs.FORC.2026.18},
  annote =	{Keywords: Differential privacy, computational geometry, width approximation, private algorithms}
}
Document
FPT Approximations for Capacitated Sum of Radii and Diameters

Authors: Arnold Filtser and Ameet Gadekar

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


Abstract
The Capacitated Sum of Radii problem involves partitioning a set of points P, where each point p ∈ P has capacity U_p, into k clusters that minimize the sum of cluster radii, such that the number of points in the cluster centered at point p is at most U_p. We begin by showing that the problem is APX-hard, and that under gap-ETH there is no parameterized approximation scheme (FPT-AS). We then construct a ≈5.83-approximation algorithm in FPT time (improving a previous ≈7.61 approximation in FPT time). Our results also hold when the objective is a general monotone symmetric norm of radii. We also improve the approximation factors for the uniform capacity case, and for the closely related problem of Capacitated Sum of Diameters.

Cite as

Arnold Filtser and Ameet Gadekar. FPT Approximations for Capacitated Sum of Radii and Diameters. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{filtser_et_al:LIPIcs.SoCG.2026.48,
  author =	{Filtser, Arnold and Gadekar, Ameet},
  title =	{{FPT Approximations for Capacitated Sum of Radii and Diameters}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{48:1--48:18},
  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.2026.48},
  URN =		{urn:nbn:de:0030-drops-258545},
  doi =		{10.4230/LIPIcs.SoCG.2026.48},
  annote =	{Keywords: clustering, sum of radii, sum of diameter, capacitated clustering, fpt}
}
Document
Dynamic Light Spanners in Doubling Metrics

Authors: Sujoy Bhore, Jonathan Conroy, and Arnold Filtser

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


Abstract
A t-spanner of a point set X in a metric space (𝒳, δ) is a graph G with vertex set P such that, for any pair of points u,v ∈ X, the distance between u and v in G is at most t times δ(u,v). We study the problem of maintaining a spanner for a dynamic point set X - that is, when X undergoes a sequence of insertions and deletions - in a metric space of constant doubling dimension. For any constant ε > 0, we maintain a (1+ε)-spanner of P whose total weight remains within a constant factor of the weight of the minimum spanning tree of X. Each update (insertion or deletion) can be performed in poly(log Φ) time, where Φ denotes the aspect ratio of X. Prior to our work, no efficient dynamic algorithm for maintaining a light-weight spanner was known even for point sets in low-dimensional Euclidean space.

Cite as

Sujoy Bhore, Jonathan Conroy, and Arnold Filtser. Dynamic Light Spanners in Doubling Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.13,
  author =	{Bhore, Sujoy and Conroy, Jonathan and Filtser, Arnold},
  title =	{{Dynamic Light Spanners in Doubling Metrics}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{13:1--13:16},
  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.2026.13},
  URN =		{urn:nbn:de:0030-drops-258193},
  doi =		{10.4230/LIPIcs.SoCG.2026.13},
  annote =	{Keywords: Dynamic data structures, spanners, light-weight, Euclidean metrics, doubling metrics}
}
Document
One Action Too Many: Inapproximability of Budgeted Combinatorial Contracts

Authors: Michal Feldman, Yoav Gal-Tzur, Tomasz Ponitka, and Maya Schlesinger

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


Abstract
We study multi-agent contract design with combinatorial actions, under budget constraints, and for a broad class of objective functions, including profit (principal’s utility), reward, and welfare. Our first result is a strong impossibility: For submodular reward functions, no randomized poly-time algorithm can approximate the optimal budget-feasible value within any finite factor, even with demand-oracle access. This result rules out extending known constant-factor guarantees from either (i) unbudgeted settings with combinatorial actions or (ii) budgeted settings with binary actions, to their combination. The hardness is tight: It holds even when all but one agent have binary actions and the remaining agent has just one additional action. On the positive side, we show that gross substitutes rewards (a well-studied strict subclass of submodular functions) admit a deterministic poly-time O(1)-approximation, using only value queries. Our results thus draw the first sharp separation between budgeted and unbudgeted settings in combinatorial contracts, and identifies gross substitutes as a tractable frontier for budgeted combinatorial contracts. Finally, we present an FPTAS for additive rewards, demonstrating that arbitrary approximation is tractable under any budget. This constitutes the first FPTAS for the multi-agent combinatorial-actions setting, even in the absence of budget constraints.

Cite as

Michal Feldman, Yoav Gal-Tzur, Tomasz Ponitka, and Maya Schlesinger. One Action Too Many: Inapproximability of Budgeted Combinatorial Contracts. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 58:1-58:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{feldman_et_al:LIPIcs.ITCS.2026.58,
  author =	{Feldman, Michal and Gal-Tzur, Yoav and Ponitka, Tomasz and Schlesinger, Maya},
  title =	{{One Action Too Many: Inapproximability of Budgeted Combinatorial Contracts}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{58:1--58:24},
  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.2026.58},
  URN =		{urn:nbn:de:0030-drops-253459},
  doi =		{10.4230/LIPIcs.ITCS.2026.58},
  annote =	{Keywords: Combinatorial Contracts, Algorithmic Contract Design, Budget-Feasible Contracts}
}
Document
Limitations to Computing Quadratic Functions on Reed-Solomon Encoded Data

Authors: Keller Blackwell and Mary Wootters

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


Abstract
We study the problem of low-bandwidth non-linear computation on Reed-Solomon encoded data. Given an [n,k] Reed-Solomon encoding of a message vector 𝐟 ∈ 𝔽_q^k, and a polynomial g ∈ 𝔽_q[X₁, X₂, …, X_k], a user wishing to evaluate g(𝐟) is given local query access to each codeword symbol. The query response is allowed to be the output of an arbitrary function evaluated locally on the codeword symbol, and the user’s aim is to minimize the total information downloaded in order to compute g(𝐟). This problem has been studied before for linear functions g; in this work we initiate the study of non-linear functions by starting with quadratic monomials. For q = p^e and distinct i,j ∈ [k], we show that any scheme evaluating the quadratic monomial g_{i,j} := X_i X_j must download at least 2 log₂(q-1) - 3 bits of information when p is an odd prime, and at least 2log₂(q-2) -4 bits when p = 2. When k = 2, our result shows that one cannot do significantly better than the naive bound of k log₂(q) bits, which is enough to recover all of 𝐟. This contrasts sharply with prior work for low-bandwidth evaluation of linear functions g(𝐟) over Reed-Solomon encoded data, for which it is possible to substantially improve upon this bound [Venkatesan Guruswami and Mary Wootters, 2016; Tamo et al., 2018; Shutty and Wootters, 2021; Kiah et al., 2024; Con and Tamo, 2022]. Some proofs have been omitted from this extended abstract; the full version can be found at [Keller Blackwell and Mary Wootters, 2025].

Cite as

Keller Blackwell and Mary Wootters. Limitations to Computing Quadratic Functions on Reed-Solomon Encoded Data. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 19:1-19:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{blackwell_et_al:LIPIcs.ITCS.2026.19,
  author =	{Blackwell, Keller and Wootters, Mary},
  title =	{{Limitations to Computing Quadratic Functions on Reed-Solomon Encoded Data}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{19:1--19:23},
  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.2026.19},
  URN =		{urn:nbn:de:0030-drops-253064},
  doi =		{10.4230/LIPIcs.ITCS.2026.19},
  annote =	{Keywords: Distributed computation, Reed-Solomon codes}
}
Document
Dimension Reduction for Clustering: The Curious Case of Discrete Centers

Authors: Shaofeng H.-C. Jiang, Robert Krauthgamer, Shay Sapir, Sandeep Silwal, and Di Yue

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


Abstract
The Johnson-Lindenstrauss transform is a fundamental method for dimension reduction in Euclidean spaces, that can map any dataset of n points into dimension O(log n) with low distortion of their distances. This dimension bound is tight in general, but one can bypass it for specific problems. Indeed, tremendous progress has been made for clustering problems, especially in the continuous setting where centers can be picked from the ambient space ℝ^d. Most notably, for k-median and k-means, the dimension bound was improved to O(log k) [Makarychev, Makarychev and Razenshteyn, STOC 2019]. We explore dimension reduction for clustering in the discrete setting, where centers can only be picked from the dataset, and present two results that are both parameterized by the doubling dimension of the dataset, denoted as ddim. The first result shows that dimension O_{ε}(ddim + log k + log log n) suffices, and is moreover tight, to guarantee that the cost is preserved within factor 1±ε for every set of centers. Our second result eliminates the log log n term in the dimension through a relaxation of the guarantee (namely, preserving the cost only for all approximately-optimal sets of centers), which maintains its usefulness for downstream applications. Overall, we achieve strong dimension reduction in the discrete setting, and find that it differs from the continuous setting not only in the dimension bound, which depends on the doubling dimension, but also in the guarantees beyond preserving the optimal value, such as which clusterings are preserved.

Cite as

Shaofeng H.-C. Jiang, Robert Krauthgamer, Shay Sapir, Sandeep Silwal, and Di Yue. Dimension Reduction for Clustering: The Curious Case of Discrete Centers. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 82:1-82:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{jiang_et_al:LIPIcs.ITCS.2026.82,
  author =	{Jiang, Shaofeng H.-C. and Krauthgamer, Robert and Sapir, Shay and Silwal, Sandeep and Yue, Di},
  title =	{{Dimension Reduction for Clustering: The Curious Case of Discrete Centers}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{82:1--82:23},
  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.2026.82},
  URN =		{urn:nbn:de:0030-drops-253698},
  doi =		{10.4230/LIPIcs.ITCS.2026.82},
  annote =	{Keywords: dimension reduction, clustering, k-median, k-means, doubling dimension}
}
Document
Additive, Near-Additive, and Multiplicative Approximations for APSP in Weighted Undirected Graphs: Trade-Offs and Algorithms

Authors: Liam Roditty and Ariel Sapir

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)


Abstract
We present a +2∑_{i=1}^{k+1} W_i-APASP algorithm for dense weighted graphs with a runtime of Õ(n^{2+1/(3k+2)), where W_i is the weight of an i^th heaviest edge on a shortest path between two vertices. Dor, Halperin and Zwick [FOCS'96 and SICOMP'00] introduced two algorithms for the commensurate unweighted +2⋅ (k+1)-APASP problem: one for sparse graphs with a runtime of Õ(n^{2-1/(k+2)} m^{1/(k+2)}) and one for dense graphs with a runtime of Õ(n^{2+1/(3k+2)}). Subsequently, Cohen and Zwick [SODA'97 and JALG'01] adapted the algorithm for sparse graphs to the weighted setting, namely a +2∑_{i=1}^{k+1} W_i-APASP algorithm with the same Õ(n^{2-1/(k+2)} m^{1/(k+2)}) runtime. We fill the nearly three decades old gap by providing an algorithm for dense weighted graphs, matching the runtime for the unweighted setting. In addition, we explore nearly additive APASP, where the multiplicative stretch is 1+ε. We present a (1+ε, min{2W₁,4W₂})-APASP algorithm with a runtime of Õ((1/ε)^{O(1)} ⋅ n^{2.15135313} ⋅ log W). This improves upon Saha and Ye [SODA'24], which had the same runtime, yet (1+ε, 2W₁)-APASP. For pure multiplicative APASP, we present a (7/3+ε)-APASP algorithm with a runtime of Õ((1/ε)^{O(1)} ⋅ n^{2.15135313} ⋅ log W). This improves, for dense graphs, the Õ(nm^{2/3}+n²) runtime of the 7/3-APASP algorithm by Baswana and Kavitha [FOCS'06 and SICOMP'10], at the cost of introducing an additional ε to the multiplicative stretch. We further view this result in a broader framework of ((3𝓁+4)/(𝓁+2) + ε)-APASP algorithms, similarly to the family of (3𝓁+4)/(𝓁+2)-APASP algorithms by Akav and Roditty [ESA'21]. This also generalizes the (2+ε)-APASP algorithm by Dory, Forster, Kirkpatrick, Nazari, Vassilevska Williams, and de Vos [SODA'24]. Finally, we show that it is possible to "bypass" an Ω̃ (n^ω) conditional lower bound by Dor, Halperin, and Zwick for α-APASP with α < 2, by allowing an additive component to the approximation (e.g. a ((6k+3)/(3k+2),∑_{i=1}^{k+1} W_i)-APASP with Õ(n^{2+1/(3k+2)}) runtime.).

Cite as

Liam Roditty and Ariel Sapir. Additive, Near-Additive, and Multiplicative Approximations for APSP in Weighted Undirected Graphs: Trade-Offs and Algorithms. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 50:1-50:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{roditty_et_al:LIPIcs.FSTTCS.2025.50,
  author =	{Roditty, Liam and Sapir, Ariel},
  title =	{{Additive, Near-Additive, and Multiplicative Approximations for APSP in Weighted Undirected Graphs: Trade-Offs and Algorithms}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{50:1--50:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.50},
  URN =		{urn:nbn:de:0030-drops-251309},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.50},
  annote =	{Keywords: Graph, Shortest Paths, Weighted Graphs, Approximation, Undirected, Single Source Shortest-Paths, Multi-Source Shortest-Paths, All-Pairs Shortest-Paths, SSSP, MSSP, MSASP, APSP, APASP}
}
Document
New Approximate Distance Oracles and Their Applications

Authors: Avi Kadria and Liam Roditty

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


Abstract
Let G = (V, E) be an undirected graph with n vertices and m edges, and let μ = m/n. A distance oracle is a data structure designed to answer approximate distance queries, with the goal of achieving low stretch, efficient space usage, and fast query time. While much of the prior work focused on distance oracles with constant query time, this paper presents a comprehensive study of distance oracles with non-constant query time. We explore the tradeoffs between space, stretch, and query time of distance oracles in various regimes. Specifically, we consider both weighted and unweighted graphs in the regimes of stretch < 2 and stretch ≥ 2. In addition, we demonstrate several applications of our new distance oracles to the n-Pairs Shortest Paths (n-PSP) problem and the All Nodes Shortest Cycles (ANSC) problem. Our main contributions are: - Weighted graphs: We present a new three-way trade-off between stretch, space, and query time, offering a natural extension of the classical Thorup–Zwick distance oracle [STOC’01 and JACM’05] to regimes with larger query time. Specifically, for any 0 < r < 1/2 and integer k ≥ 1, we construct a (2k(1 - 2r) - 1)-stretch distance oracle with Õ(m + n^{1 + 1/k}) space and Õ(μ n^r) query time. This construction provides an asymptotic improvement over the classical (2k - 1)-stretch and O(n^{1 + 1/k})-space tradeoff of Thorup and Zwick in sparse graphs, at the cost of increased query time. We also improve upon a result of Dalirrooyfard et al. [FOCS’22], who presented a (2k - 2)-stretch distance oracle with O(m + n^{1 + 1/k}) space and O(μ n^{1/k}) query time. In our oracle we reduce the stretch from (2k - 2) to (2k - 5) while preserving the same space and query time. - Unweighted graphs: We present a (2k - 5, 4 + 2_{odd})-approximation distance oracle with O(n^{1 + 1/k}) space and O(n^{1/k}) query time. This improves upon a (2k - 2, 2_{odd})-approximation distance oracle of Dalirrooyfard et al. [FOCS’22] while maintaining the same space and query time. We also present a distance oracle that given u,v ∈ V returns an estimate d̂(u,v) ≤ d(u,v) + 2⌈ d(u,v) / 3 ⌉ + 2, using O(n^{4/3 + 2ε}) space and O(n^{1 - 3ε}) query time. To the best of our knowledge, this is the first distance oracle that simultaneously achieves a multiplicative stretch < 2, and a space complexity O(n^{1.5 - α}), for some α > 0. - Applications for n-PSP and ANSC: We present an Õ(m^{1 - 1/(k+1)} n)-time algorithm for the n-PSP problem, that for every input pair ⟨s_i,t_i⟩, where i ∈ [n], returns an estimate d̂(s_i, t_i) such that d̂(s_i,t_i) ≤ d(s_i,t_i) + 2⌈d(s_i,t_i)/2k⌉. By allowing a small additive error, this result circumvents the conditional running time lower bound of Ω(m^{2 - 2/(k+1)} ⋅ n^{1/(k+1) - o(1)}), established by Dalirrooyfard et al. [FOCS’22] for achieving (1 + 1/k)-stretch. Additionally, we present an Õ(mn^{1 - 1/k})-time algorithm for the ANSC problem that computes, for every u ∈ V, an estimate ĉ_u such that ĉ_u ≤ SC(u) + 2⌈SC(u)/2(k - 1)⌉, where SC(u) denotes the length of the shortest cycle containing u. This improves upon the Õ(m^{2 - 2/k}n^{1/k})-time algorithm of Dalirrooyfard et al. [FOCS'22], while achieving the same approximation guarantee. We obtain our results by developing several new techniques, among them are the borderline vertices technique and the middle vertex technique, which may be of independent interest.

Cite as

Avi Kadria and Liam Roditty. New Approximate Distance Oracles and Their Applications. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{kadria_et_al:LIPIcs.ISAAC.2025.43,
  author =	{Kadria, Avi and Roditty, Liam},
  title =	{{New Approximate Distance Oracles and Their Applications}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{43:1--43:17},
  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.2025.43},
  URN =		{urn:nbn:de:0030-drops-249514},
  doi =		{10.4230/LIPIcs.ISAAC.2025.43},
  annote =	{Keywords: Distance oracles, Fine-grained algorithms, Graph algorithms, Data structures}
}
Document
Optimal Online Bipartite Matching in Degree-2 Graphs

Authors: Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha

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


Abstract
Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of 1-1/e. In this work, we study classes of graphs where the online degree is restricted to 2. As expected, one can achieve a competitive ratio of better than 1-1/e in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a 0.75 competitive ratio algorithm is optimal. We show that the folklore Half-Half algorithm achieves a competitive ratio of η ≈ 0.717772… and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.

Cite as

Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha. Optimal Online Bipartite Matching in Degree-2 Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{bhangale_et_al:LIPIcs.ISAAC.2025.13,
  author =	{Bhangale, Amey and Chakraborty, Arghya and Harsha, Prahladh},
  title =	{{Optimal Online Bipartite Matching in Degree-2 Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{13:1--13:19},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-249216},
  doi =		{10.4230/LIPIcs.ISAAC.2025.13},
  annote =	{Keywords: Online Algorithm, Bipartite matching}
}
Document
NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks

Authors: Ilan Hartskeerl, Tamara Mchedlidze, Simon van Wageningen, Peter Vangorp, and Alexandru Telea

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)


Abstract
tsNET is a recent graph drawing (GD) method that creates high quality layouts but suffers from a very high runtime. We present a new GD method, NNP-NET, which reduces tsNET’s time complexity to generate layouts for very large graphs in seconds. Additionally, we extend tsNET to support drawing graphs with edge weights. We accomplish this by replacing tsNET’s t-SNE projection with Neural Network Projection (NNP), a fast dimensionality reduction (DR) method that can imitate any given DR method. Our experiments show that NNP-NET gets good quality results when compared to other state-of-the art GD methods while yielding a better computational scalability.

Cite as

Ilan Hartskeerl, Tamara Mchedlidze, Simon van Wageningen, Peter Vangorp, and Alexandru Telea. NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{hartskeerl_et_al:LIPIcs.GD.2025.22,
  author =	{Hartskeerl, Ilan and Mchedlidze, Tamara and van Wageningen, Simon and Vangorp, Peter and Telea, Alexandru},
  title =	{{NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.22},
  URN =		{urn:nbn:de:0030-drops-250087},
  doi =		{10.4230/LIPIcs.GD.2025.22},
  annote =	{Keywords: supervised graph drawing, dimensionality reduction, t-SNE}
}
Document
Hierarchical Consensus: Scalability Through Optimism and Weak Liveness

Authors: Pedro Antonino, Antoine Durand, and A. W. Roscoe

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)


Abstract
Scalability is a central concern of Byzantine Fault Tolerant (BFT) distributed protocols. The ubiquitous approach to work around the well-known Dolev-Reischuk Ω(n²) communication complexity lower bound is to use a random selection process to draw a hopefully small committee from a population of agents to run the communication-heavy protocol. We propose a notion of hierarchical consensus that combines two sub-protocols: an optimistic primary sub-protocol that can tolerate less than 1/2 failures and a fallback secondary protocol that can tolerate less than 1/3 failures; we achieve the higher failure threshold by requiring a weaker notion of liveness for the primary. This distinction between the level of fault tolerance between primary and secondary is reflected in the size of committees implementing these protocols. For a population of agents with close to 2/3 of honest agents, we need to select a committee with hundreds of agents to reach the level of tolerance expected for the primary, whereas we need thousands to reach the level expected for the secondary with a very small probability of error ε. Our hierarchical construct is such that if the primary comes to a decision, it can simply propagate it to the secondary protocol, so it does not need to properly engage in an agreement protocol independently. Our architecture is flexible and allows us to use our technique for most protocols that are based on random sampling. By studying hierarchical protocols, we discovered new theoretical results of independent interest. Specifically, the ability to handover from a primary protocol requires a new Justifiability property that allows agents to pre-decide on a value, such that if the protocol decides, it must be on that pre-decided value.

Cite as

Pedro Antonino, Antoine Durand, and A. W. Roscoe. Hierarchical Consensus: Scalability Through Optimism and Weak Liveness. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{antonino_et_al:LIPIcs.DISC.2025.6,
  author =	{Antonino, Pedro and Durand, Antoine and Roscoe, A. W.},
  title =	{{Hierarchical Consensus: Scalability Through Optimism and Weak Liveness}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.6},
  URN =		{urn:nbn:de:0030-drops-248232},
  doi =		{10.4230/LIPIcs.DISC.2025.6},
  annote =	{Keywords: Hierarchical, Handover, Justifiability, Consensus, Distributed Systems, Blockchain}
}
Document
Towards Optimal Distributed Edge Coloring with Fewer Colors

Authors: Manuel Jakob, Yannic Maus, and Florian Schager

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)


Abstract
There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem: while (2Δ-1)-edge coloring - where Δ is the maximum degree - can be solved in 𝒪(log^{∗}(n)) rounds on constant-degree graphs, the seemingly minor reduction to (2Δ-2) colors leads to an Ω(log n) lower bound [Chang, He, Li, Pettie & Uitto, SODA'18]. Understanding this sharp divide between very local problems and inherently more global ones remains a central open question in distributed computing and it is a core focus of this paper. As our main contribution we design a deterministic distributed 𝒪(log n)-round reduction from the (2Δ-2)-edge coloring problem to the much easier (2Δ-1)-edge coloring problem. This reduction is optimal, as the (2Δ-2)-edge coloring problem admits an Ω(log n) lower bound that even holds on the class of constant-degree graphs, whereas the 2Δ-1-edge coloring problem can be solved in 𝒪(log^{∗}n) rounds. By plugging in the (2Δ-1)-edge coloring algorithms from [Balliu, Brandt, Kuhn & Olivetti, PODC'22] running in 𝒪(log^{12}Δ + log^{∗} n) rounds, we obtain an optimal runtime of 𝒪(log n) rounds as long as Δ = 2^{𝒪(log^{1/12} n)}. Previously, such an optimal algorithm was only known for the class of constant-degree graphs [Brandt, Maus, Narayanan, Schager & Uitto, SODA'25]. Furthermore, on general graphs our reduction improves the runtime from 𝒪̃(log³ n) to 𝒪̃(log^{5/3} n). In addition, we also obtain an optimal 𝒪(log log n)-round randomized reduction of (2Δ - 2)-edge coloring to (2Δ - 1)-edge coloring. This leads to a 𝒪̃(log^{5/3} log n)-round (2Δ-2)-edge coloring algorithm, which beats the (very recent) previous state-of-the-art taking 𝒪̃(log^{8/3}log n) rounds from [Bourreau, Brandt & Nolin, STOC'25]. Lastly, we obtain an 𝒪(log_Δ n)-round reduction from the (2Δ-1)-edge coloring, albeit to the somewhat harder maximal independent set (MIS) problem.

Cite as

Manuel Jakob, Yannic Maus, and Florian Schager. Towards Optimal Distributed Edge Coloring with Fewer Colors. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 37:1-37:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{jakob_et_al:LIPIcs.DISC.2025.37,
  author =	{Jakob, Manuel and Maus, Yannic and Schager, Florian},
  title =	{{Towards Optimal Distributed Edge Coloring with Fewer Colors}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{37:1--37:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.37},
  URN =		{urn:nbn:de:0030-drops-248547},
  doi =		{10.4230/LIPIcs.DISC.2025.37},
  annote =	{Keywords: distributed graph algorithms, edge coloring, LOCAL model}
}
Document
Composable Byzantine Agreements with Reorder Attacks

Authors: Jing Chen, Jin Dong, Jichen Li, Xuanzhi Xia, and Wentao Zhou

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)


Abstract
Byzantine agreement (BA) is a foundational building block in distributed systems that has been extensively studied for decades. With the growing demand for protocol composition in practice, the security analysis of BA protocols under multi-instance executions has attracted increasing attention. However, most existing adversary models focus solely on party corruption and neglect important threats posed by adversarial manipulations of communication channels in the network. Through channel attacks, messages can be reordered across multiple executions and lead to violations of the protocol’s security guarantees, without the participating parties being corrupted. In this work, we present the first adversary model that combines party corruption and channel attacks. Based on this model, we establish new security thresholds for Byzantine agreement under parallel and concurrent compositions, supported by complementary impossibility and possibility results that match each other to form a tight bound. For the impossibility result, we show that even authenticated Byzantine agreement protocols cannot be secure under parallel composition when n ≤ 3t or n ≤ 2c + 2t + 1, where t and c denote the number of corrupted parties and communication channels, respectively. For the possibility result, we prove the existence of secure protocols for unauthenticated Byzantine agreement under parallel and concurrent composition, when n > 3t and n > 2c+2t+1. More specifically, we provide a general black-box compiler that transforms any single-instance secure BA protocol into one that is secure under parallel executions, and we provide a non-black-box construction for concurrent compositions.

Cite as

Jing Chen, Jin Dong, Jichen Li, Xuanzhi Xia, and Wentao Zhou. Composable Byzantine Agreements with Reorder Attacks. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{chen_et_al:LIPIcs.AFT.2025.13,
  author =	{Chen, Jing and Dong, Jin and Li, Jichen and Xia, Xuanzhi and Zhou, Wentao},
  title =	{{Composable Byzantine Agreements with Reorder Attacks}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.13},
  URN =		{urn:nbn:de:0030-drops-247321},
  doi =		{10.4230/LIPIcs.AFT.2025.13},
  annote =	{Keywords: Byzantine agreement, protocol composition, channel reorder attack, security threshold}
}
Document
RANDOM
Bit-Fixing Extractors for Almost-Logarithmic Entropy

Authors: Dean Doron and Ori Fridman

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


Abstract
An oblivious bit-fixing source is a distribution over {0,1}ⁿ, where k bits are uniform and independent and the rest n-k are fixed a priori to some constant value. Extracting (close to) true randomness from an oblivious bit-fixing source has been studied since the 1980s, with applications in cryptography and complexity theory. We construct explicit extractors for oblivious bit-fixing source that support k = Õ(log n), outputting almost all the entropy with low error. The previous state-of-the-art construction that outputs many bits is due to Rao [Rao, CCC '09], and requires entropy k ≥ log^{c} n for some large constant c. The two key components in our constructions are new low-error affine condensers for poly-logarithmic entropies (that we achieve using techniques from the nonmalleable extractors literature), and a dual use of linear condensers for OBF sources.

Cite as

Dean Doron and Ori Fridman. Bit-Fixing Extractors for Almost-Logarithmic Entropy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.33,
  author =	{Doron, Dean and Fridman, Ori},
  title =	{{Bit-Fixing Extractors for Almost-Logarithmic Entropy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{33:1--33:19},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-243994},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.33},
  annote =	{Keywords: Seedless extractors, oblivious bit-fixing sources}
}
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