123 Search Results for "Wu, Yi"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.112
Towards Tight Robust Coresets for k-Medians Clustering

Authors: Lingxiao Huang, Zhenyu Jiang, Yi Li, and Xuan Wu

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

Abstract
This paper considers coresets for the robust k-medians problem with m outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension d, the coreset size is O(m) + Õ(kdε^{-2}), which is optimal up to logarithmic factors. For Euclidean spaces, the coreset size is O(mε^{-1}) + Õ(min{k^{4/3}ε^{-2}, kε^{-3}}), improving upon a recent result by Jiang and Lou (ICALP 2025). These results also extend to robust (k,z)-clustering, yielding, for VC and doubling dimension, a coreset size of O(m) + Õ(kdε^{-2z}) with the optimal linear dependence on m. This extended result improves upon the earlier work of Huang et al. (SODA 2025). The techniques introduce novel dataset decompositions, enabling chaining arguments to be applied jointly across multiple components.
Cite as

Lingxiao Huang, Zhenyu Jiang, Yi Li, and Xuan Wu. Towards Tight Robust Coresets for k-Medians Clustering. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 112:1-112:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{huang_et_al:LIPIcs.ICALP.2026.112,
  author =	{Huang, Lingxiao and Jiang, Zhenyu and Li, Yi and Wu, Xuan},
  title =	{{Towards Tight Robust Coresets for k-Medians Clustering}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{112:1--112:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.112},
  URN =		{urn:nbn:de:0030-drops-265013},
  doi =		{10.4230/LIPIcs.ICALP.2026.112},
  annote =	{Keywords: robust coresets, clustering, k-medians}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.16
Online Hitting Set for Axis-Aligned Squares

Authors: Minati De, Satyam Singh, and Csaba D. Tóth

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

Abstract
Given a set P of n points in the plane and a sequence of axis-aligned squares that arrive in an online fashion, the online hitting set problem consists of maintaining, by adding new points from P if necessary, a hitting set H ⊆ P, which contains at least one point in every input square that has already arrived. We present an O(log n)-competitive deterministic algorithm for this problem. The competitive ratio is the best possible, apart from constant factors. In fact, this is the first O(log n)-competitive algorithm for the online hitting set problem that works for geometric objects of arbitrary sizes (i.e., unbounded scaling factors) in the plane. We further generalize this result to positive homothets of a polygon with k ≥ 3 vertices in the plane and provide an O(k²log n)-competitive algorithm.
Cite as

Minati De, Satyam Singh, and Csaba D. Tóth. Online Hitting Set for Axis-Aligned Squares. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{de_et_al:LIPIcs.SWAT.2026.16,
  author =	{De, Minati and Singh, Satyam and T\'{o}th, Csaba D.},
  title =	{{Online Hitting Set for Axis-Aligned Squares}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.16},
  URN =		{urn:nbn:de:0030-drops-260528},
  doi =		{10.4230/LIPIcs.SWAT.2026.16},
  annote =	{Keywords: axis-aligned squares, hitting set, homothets of a polygon, online algorithm}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.27
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
DOI: 10.4230/LIPIcs.FORC.2026.7
When to Ask a Question: Understanding Communication Strategies in Generative AI Tools

Authors: Charlotte Park, Kate Donahue, and Manish Raghavan

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

Abstract
Generative AI models differ from traditional machine learning tools in that they allow users to provide as much or as little information as they choose in their inputs. This flexibility often leads users to omit certain details, relying on the models to infer and fill in under-specified information based on distributional knowledge of user preferences. Such inferences may privilege majority viewpoints and disadvantage users with atypical preferences, raising concerns about fairness. Unlike more traditional recommender systems, LLMs can explicitly solicit more information from users through natural language. However, while directly eliciting user preferences could increase personalization and mitigate inequality, excessive querying places a burden on users who value efficiency. We develop a stylized model of user-LLM interaction and develop an objective that captures tradeoff between user burden and preference representation. Building on the observation that individual preferences are often correlated, we analyze how AI systems should balance inference and elicitation, characterizing the optimal amount of information to solicit before content generation. Ultimately, we show that information elicitation can mitigate the systematic biases of preference inference, enabling the design of generative tools that better incorporate diverse user perspectives while maintaining efficiency. We complement this theoretical analysis with an empirical evaluation illustrating the model’s predictions and exploring their practical implications.
Cite as

Charlotte Park, Kate Donahue, and Manish Raghavan. When to Ask a Question: Understanding Communication Strategies in Generative AI Tools. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 7:1-7:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{park_et_al:LIPIcs.FORC.2026.7,
  author =	{Park, Charlotte and Donahue, Kate and Raghavan, Manish},
  title =	{{When to Ask a Question: Understanding Communication Strategies in Generative AI Tools}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{7:1--7:25},
  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.2026.7},
  URN =		{urn:nbn:de:0030-drops-259782},
  doi =		{10.4230/LIPIcs.FORC.2026.7},
  annote =	{Keywords: human-AI interaction, user modeling, personalization}
}
Document
DOI: 10.4230/LIPIcs.FORC.2026.15
Incentivizing High-Quality Content in Online Recommender Systems

Authors: Xinyan Hu, Meena Jagadeesan, Michael I. Jordan, and Jacob Steinhardt

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

Abstract
In content recommender systems such as TikTok and YouTube, the platform’s recommendation algorithm shapes content producer incentives. Many platforms employ online learning, which generates intertemporal incentives, since content produced today affects recommendations of future content. We study the game between producers and analyze the content created at equilibrium. We prove that standard online learning algorithms, such as Hedge and EXP3, unfortunately incentivize producers to create low-quality content, where producers' effort approaches zero in the long run for typical learning rate schedules. Motivated by this negative result, we design learning algorithms that incentivize producers to invest high effort and achieve high user welfare. At a conceptual level, our work illustrates the unintended impact that a platform’s learning algorithm can have on content quality and introduces algorithmic approaches to mitigating these effects.
Cite as

Xinyan Hu, Meena Jagadeesan, Michael I. Jordan, and Jacob Steinhardt. Incentivizing High-Quality Content in Online Recommender Systems. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hu_et_al:LIPIcs.FORC.2026.15,
  author =	{Hu, Xinyan and Jagadeesan, Meena and Jordan, Michael I. and Steinhardt, Jacob},
  title =	{{Incentivizing High-Quality Content in Online Recommender Systems}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{15:1--15:18},
  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.2026.15},
  URN =		{urn:nbn:de:0030-drops-259887},
  doi =		{10.4230/LIPIcs.FORC.2026.15},
  annote =	{Keywords: recommender systems, content quality, producer incentives, online learning, algorithmic game theory, Stackelberg games}
}
Document
DOI: 10.4230/LIPIcs.FORC.2026.20
Privacy, Prediction, and Allocation

Authors: Ben Jacobsen and Nitin Kohli

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

Abstract
Algorithmic predictions are increasingly used to inform the allocation of scarce resources. The promise of these methods is that, through machine learning, they can better identify the people who would benefit most from interventions. Recently, however, several works have called this assumption into question by demonstrating the existence of settings where simple, unit-level allocation strategies can meet or even exceed the performance of those based on individual-level targeting. Separately, other works have objected to individual-level targeting on privacy grounds, leading to an unusual situation where a single solution, unit-level targeting, is recommended for reasons of both privacy and utility. Motivated by the desire to fully understand the interplay of privacy and targeting levels, we initiate the study of aid allocation systems that satisfy differential privacy, synthesizing existing works on private optimization with the economic models of aid allocation used in the non-private literature. To this end, we investigate private variants of both individual and unit-level allocation strategies in both stochastic and distribution-free settings under a range of constraints on data availability. Through this analysis, we provide clean, interpretable bounds characterizing the tradeoffs between privacy, efficiency, and targeting precision in allocation.
Cite as

Ben Jacobsen and Nitin Kohli. Privacy, Prediction, and Allocation. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 20:1-20:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jacobsen_et_al:LIPIcs.FORC.2026.20,
  author =	{Jacobsen, Ben and Kohli, Nitin},
  title =	{{Privacy, Prediction, and Allocation}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{20:1--20:24},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-259935},
  doi =		{10.4230/LIPIcs.FORC.2026.20},
  annote =	{Keywords: Differential privacy, fair allocation, limits of prediction}
}
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.2026.71
Approximating Euclidean Shallow-Light Trees

Authors: Hung Le, Shay Solomon, Cuong Than, Csaba D. Tóth, and Tianyi Zhang

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

Abstract
For a weighted graph G = (V, E, w) and a designated source vertex s ∈ V, a spanning tree that simultaneously approximates a shortest-path tree w.r.t. source s and a minimum spanning tree is called a shallow-light tree (SLT). Specifically, an (α, β)-SLT of G w.r.t. s ∈ V is a spanning tree of G with root-stretch α (preserving all distances between s and all other vertices up to a factor of α) and lightness β (its weight is at most β times the weight of a minimum spanning tree of G). It was shown in the early 1990s that (1) for any graph, any source, and any ε > 0, there is a (1 + ε, O(1/ε))-SLT, and (2) there exist graphs for which β = Ω(1/ε) for any (1+ε,β)-SLT. The focus of this work is on SLTs in low-dimensional Euclidean spaces, which are of special interest for some applications of SLTs, in geometric network optimization problems. The aforementioned existential lower bound applies to Euclidean plane, as well. It was shown more than a decade ago that (1) by using Steiner points, one can reduce the lightness bound from O(1/ε) to O(√{1/ε}), and (2) there exist point sets in the plane for which β = Ω(√{1/ε}) for any Steiner (1+ε,β)-SLT. These tight existential bounds for the Euclidean case yield approximation factors of O(1/ε) and O(√{1/ε}) on the minimum weight of any non-Steiner and Steiner tree with root-stretch 1+ε, respectively. Despite the large body of work on SLTs, the basic question of whether a better approximation algorithm exists was left untouched to date, and this holds in any graph family. This paper makes a first nontrivial step towards resolving this question by presenting two bicriteria approximation algorithms. For any ε > 0, a set P of n points in constant-dimensional Euclidean space and a source s ∈ P, our first (respectively, second) algorithm returns, in O(n log n ⋅ polylog(ε^{-1})) time, a non-Steiner (resp., Steiner) tree with root-stretch 1+O(ε log ε^{-1}) and weight at most O(opt_ε ⋅ log² ε^{-1}) (resp., O(opt_ε ⋅ log ε^{-1})), where opt_ε denotes the minimum weight of a non-Steiner (resp., Steiner) tree with root-stretch 1+ε.
Cite as

Hung Le, Shay Solomon, Cuong Than, Csaba D. Tóth, and Tianyi Zhang. Approximating Euclidean Shallow-Light Trees. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 71:1-71:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{le_et_al:LIPIcs.SoCG.2026.71,
  author =	{Le, Hung and Solomon, Shay and Than, Cuong and T\'{o}th, Csaba D. and Zhang, Tianyi},
  title =	{{Approximating Euclidean Shallow-Light Trees}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{71:1--71:16},
  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.2026.71},
  URN =		{urn:nbn:de:0030-drops-258789},
  doi =		{10.4230/LIPIcs.SoCG.2026.71},
  annote =	{Keywords: geometric network design, optimization, shallow-light tree, Steiner point}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.78
Mapping Chemical Space: Topological Data Analysis of Chemical Latent Space with Mapper

Authors: Dhruv Meduri, Chuan-Shen Hu, Cong Shen, Kelin Xia, and Bei Wang

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

Abstract
The vast chemical space, encompassing virtually innumerable molecules and materials, presents both immense opportunities and significant challenges. The design and discovery of novel drugs and functional materials may be viewed as a search within this space; however, the sheer scale of potential candidates renders exhaustive exploration infeasible. To address this, we introduce Chemical Mapper, a framework that integrates topological data analysis with deep learning to enable the visual exploration and analysis of chemical latent spaces. At its core, Chemical Mapper employs mapper, a widely used tool in topological data analysis, to investigate the organizational principles of chemical latent spaces defined by molecular representations learned by geometric deep learning models. In doing so, Chemical Mapper not only highlights groups of molecular representations but also uncovers the relationships among them through linkages and branching structures. Our results show that Chemical Mapper reveals intrinsic patterns associated with molecular scaffolds, functional groups, and chemical properties, as well as the structural and functional evolutions of the molecules.
Cite as

Dhruv Meduri, Chuan-Shen Hu, Cong Shen, Kelin Xia, and Bei Wang. Mapping Chemical Space: Topological Data Analysis of Chemical Latent Space with Mapper. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{meduri_et_al:LIPIcs.SoCG.2026.78,
  author =	{Meduri, Dhruv and Hu, Chuan-Shen and Shen, Cong and Xia, Kelin and Wang, Bei},
  title =	{{Mapping Chemical Space: Topological Data Analysis of Chemical Latent Space with Mapper}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{78:1--78:20},
  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.2026.78},
  URN =		{urn:nbn:de:0030-drops-258854},
  doi =		{10.4230/LIPIcs.SoCG.2026.78},
  annote =	{Keywords: Practice of computational topology, topological data analysis, applications in chemistry, mapper algorithm, high-dimensional data analysis, chemical spaces, geometric deep learning, latent space geometry}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.80
Hardness of High-Dimensional Linear Classification

Authors: Alexander Munteanu, Simon Omlor, and Jeff M. Phillips

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

Abstract
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and approximate forms. However, only O(n^d) and respectively Õ(1/ε^d) upper bounds are known and complemented by polynomial lower bounds that do not support the exponential in dimension dependence. We close this gap up to polylogarithmic terms by reduction from widely-believed hardness conjectures for Affine Degeneracy testing and k-Sum problems. Our reductions yield matching lower bounds of Ω̃(n^d) and respectively Ω̃(1/ε^d) based on Affine Degeneracy testing, and Ω̃(n^{d/2}) and respectively Ω̃(1/ε^{d/2}) conditioned on k-Sum. The first bound also holds unconditionally if the computational model is restricted to make sidedness queries, which corresponds to a widely spread setting implemented and optimized in many contemporary algorithms and computing paradigms.
Cite as

Alexander Munteanu, Simon Omlor, and Jeff M. Phillips. Hardness of High-Dimensional Linear Classification. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 80:1-80:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{munteanu_et_al:LIPIcs.SoCG.2026.80,
  author =	{Munteanu, Alexander and Omlor, Simon and Phillips, Jeff M.},
  title =	{{Hardness of High-Dimensional Linear Classification}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{80:1--80:16},
  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.2026.80},
  URN =		{urn:nbn:de:0030-drops-258871},
  doi =		{10.4230/LIPIcs.SoCG.2026.80},
  annote =	{Keywords: Conditional Hardness, k-Sum, Affine Degeneracy, Halfspace Discrepancy, Classification}
}
Document
DOI: 10.4230/LITES.11.1.1
A Survey of Real-Time Support, Analysis, and Advancements in ROS 2

Authors: Daniel Casini, Jian-Jia Chen, Jing Li, Federico Reghenzani, and Harun Teper

Published in: LITES, Volume 11, Issue 1 (2026). Leibniz Transactions on Embedded Systems, Volume 11, Issue 1

Abstract
The Robot Operating System 2 (ROS 2) has emerged as a relevant middleware framework for robotic applications, offering modularity, distributed execution, and communication. In the last six years, ROS 2 has drawn increasing attention from the real-time systems community and industry. This survey presents a comprehensive overview of research efforts that analyze, enhance, and extend ROS 2 to support real-time execution. We first provide a detailed description of the internal scheduling mechanisms of ROS 2 and its layered architecture, including the interaction with DDS-based communication and other communication middleware. We then review key contributions from the literature, covering timing analysis for both single- and multi-threaded executors, metrics such as response time, reaction time, and data age, and different communication modes. The survey also discusses community-driven enhancements to the ROS 2 runtime, including new executor algorithm designs, real-time GPU management, and microcontroller support via micro-ROS. Furthermore, we summarize techniques for bounding DDS communication delays, message filters, and profiling tools that have been developed to support analysis and experimentation. To help systematize this growing body of work, we introduce taxonomies that classify the surveyed contributions based on different criteria. This survey aims to guide both researchers and practitioners in understanding and improving the real-time capabilities of ROS 2.
Cite as

Daniel Casini, Jian-Jia Chen, Jing Li, Federico Reghenzani, and Harun Teper. A Survey of Real-Time Support, Analysis, and Advancements in ROS 2. In LITES, Volume 11, Issue 1 (2026). Leibniz Transactions on Embedded Systems, Volume 11, Issue 1, pp. 1:1-1:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{casini_et_al:LITES.11.1.1,
  author =	{Casini, Daniel and Chen, Jian-Jia and Li, Jing and Reghenzani, Federico and Teper, Harun},
  title =	{{A Survey of Real-Time Support, Analysis, and Advancements in ROS 2}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{1:1--1:37},
  ISSN =	{2199-2002},
  year =	{2026},
  volume =	{11},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.11.1.1},
  URN =		{urn:nbn:de:0030-drops-257914},
  doi =		{10.4230/LITES.11.1.1},
  annote =	{Keywords: ROS 2, middleware, real-time, timing predictability, publish-subscribe}
}
Document
DOI: 10.4230/OASIcs.FMBC.2026.5
Smart Tests for a Smart Contract Language

Authors: Miguel Valido and António Ravara

Published in: OASIcs, Volume 142, 7th International Workshop on Formal Methods for Blockchains (FMBC 2026)

Abstract
Smart contracts are high-stakes software: their immutable, publicly accessible, code may govern assets worth millions, meaning that even minor defects can have severe consequences. The most used techniques to ensure smart contract correctness are testing and formal verification. Testing is almost always employed but is often restricted to unit tests (which often miss edge cases) and has limited coverage, while formal verification can provide strong guarantees but is often costly and complex to apply, demanding substantial time and expertise. Property-based testing bridges this gap by exploring large input spaces and shrinking failures to minimal counterexamples, helping uncover defects early in development. Formal verification can be left to critical features once testing has filtered out common issues. To add to the challenges smart contract developers face, most languages used were not designed with safety and security guarantees built-in. Daml is a smart contract language designed with correctness in mind, featuring a strong static type system, functional programming paradigms, and built-in abstractions for common smart contract patterns. However, Daml currently lacks support for property-based testing, limiting developers' ability to systematically explore input spaces and verify contract properties. This paper introduces Hypothesis2Daml, an open-source library that brings property-based testing to the Daml ecosystem by connecting the Hypothesis testing framework with the Daml JSON API. Hypothesis2Daml enables developers to specify invariants, preconditions, and stateful workflows over realistic ledger interactions, while providing automatic input generation, shrinking, and isolation of ledger state between test cases. The approach is evaluated using a benchmark consisting of eight contracts, three Daml templates, and twenty-eight property-based tests covering happy paths, negative cases, and alternative interaction orders. The results show that property-based testing is feasible for Daml smart contracts, can systematically expose violated properties with minimal counterexamples, and supports effective debugging of realistic, stateful workflows.
Cite as

Miguel Valido and António Ravara. Smart Tests for a Smart Contract Language. In 7th International Workshop on Formal Methods for Blockchains (FMBC 2026). Open Access Series in Informatics (OASIcs), Volume 142, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{valido_et_al:OASIcs.FMBC.2026.5,
  author =	{Valido, Miguel and Ravara, Ant\'{o}nio},
  title =	{{Smart Tests for a Smart Contract Language}},
  booktitle =	{7th International Workshop on Formal Methods for Blockchains (FMBC 2026)},
  pages =	{5:1--5:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-424-6},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{142},
  editor =	{Bartoletti, Massimo and Marmsoler, Diego},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FMBC.2026.5},
  URN =		{urn:nbn:de:0030-drops-257021},
  doi =		{10.4230/OASIcs.FMBC.2026.5},
  annote =	{Keywords: Smart contracts, Blockchain, Daml, Property-based testing, Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.31
A Demigod’s Number for the Rubik’s Cube

Authors: Arturo Merino and Bernardo Subercaseaux

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
It is by now well-known that any state of the 3× 3 × 3 Rubik’s Cube can be solved in at most 20 moves, a result often referred to as "God’s Number". However, this result took Rokicki et al. around 35 CPU years to prove and is therefore very challenging to reproduce. We provide a novel approach to obtain a worse bound of 36 moves with high confidence, but that offers two main advantages: (i) it is easy to understand, reproduce, and verify, and (ii) our main idea generalizes to bounding the diameter of other vertex-transitive graphs by at most twice its true value, hence the name "demigod number". Our approach is based on the fact that, for vertex-transitive graphs, the diameter at most twice the average distance (of which we give a much simpler proof than in the literature). Then, by sampling uniformly random states and using a modern solver to obtain upper bounds on their distance, a standard concentration bound allows us to confidently state that the average distance is around 18.32 ± 0.18, from where the diameter is at most 36.
Cite as

Arturo Merino and Bernardo Subercaseaux. A Demigod’s Number for the Rubik’s Cube. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{merino_et_al:LIPIcs.FUN.2026.31,
  author =	{Merino, Arturo and Subercaseaux, Bernardo},
  title =	{{A Demigod’s Number for the Rubik’s Cube}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{31:1--31:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.31},
  URN =		{urn:nbn:de:0030-drops-257505},
  doi =		{10.4230/LIPIcs.FUN.2026.31},
  annote =	{Keywords: Diameter, Rubik’s Cube, Experimental mathematics}
}
Document
Research
DOI: 10.4230/TGDK.4.1.1
On the Computational Cost of Knowledge Graph Embeddings

Authors: Victor Charpenay, Mansour Zoubeirou A Mayaki, and Antoine Zimmermann

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract
Over a decade, numerous Knowledge Graph Embedding (KGE) models have been designed and evaluated on reference datasets, always with increasing performance. In this paper, we re-evaluate these models with respect to their computational efficiency during training, by estimating the computational cost of the procedure expressed in floating-point operations. We design a cost model based on analytical expressions and apply it on a collection of 20 KGE models, representative of the state-of-the-art. We show that dimensionality or parameter efficiency, used in the literature to compare models with each other, are not suitable to evaluate the true cost of models. Through fixed-budget experiments, a novel approach to evaluate KGE models based on cost estimates, we re-assess the relative performance of model families compared to the state-of-the-art. Bilinear models such as ComplEx underperform with a low computational budget while hyperbolic linear models appear to offer no particular benefit compared to simpler Euclidian models, especially the MuRE model. Neural models, such as ConvE or CompGCN, achieve reasonable performance in the literature but their high computational cost appears unnecessary when compared with other models. The trade-off between efficiency and expressivity of both linear and neural models is to be further explored.
Cite as

Victor Charpenay, Mansour Zoubeirou A Mayaki, and Antoine Zimmermann. On the Computational Cost of Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 1:1-1:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{charpenay_et_al:TGDK.4.1.1,
  author =	{Charpenay, Victor and Zoubeirou A Mayaki, Mansour and Zimmermann, Antoine},
  title =	{{On the Computational Cost of Knowledge Graph Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:30},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.1},
  URN =		{urn:nbn:de:0030-drops-256863},
  doi =		{10.4230/TGDK.4.1.1},
  annote =	{Keywords: Knowledge Graph Embedding, Parameter Efficiency, Computational Budget, Green AI}
}
Document
DOI: 10.4230/OASIcs.NINeS.2026.7
What Obstructed Skies Teach Us About Satellite Internet

Authors: Bhaskar Kataria, Hammas Bin Tanveer, Rishab Nithyanand, and Rachee Singh

Published in: OASIcs, Volume 139, 1st New Ideas in Networked Systems (NINeS 2026)

Abstract
Low Earth Orbit satellite networks can extend Internet connectivity to remote areas where traditional broadband infrastructure is unavailable. However physical obstructions, e.g., dense forest cover, can interfere with satellite communication by blocking the user terminal’s line of sight to the satellite constellation. Unfortunately the impact of such obstructions on the connectivity of user terminals is not well studied. We bridge this gap by conducting an experimental study of how physical obstructions influence satellite network connectivity. Through controlled experiments using a purpose-built hardware testbed, we quantify the performance degradation caused by physical obstructions to user terminals. Our results show that obstructions increase round-trip latency by an average of 4% and packet loss by 0.3%. Obstructions cause user terminals to connect to a different satellite than the unobstructed terminal approximately 15% of the time. We find evidence of a previously undocumented adaptive mechanism we call responsive routing, where the satellite network switches obstructed terminals to alternative satellites within the standard 15-second interval between typical handovers. Our data is publicly available as supplementary material to this article.
Cite as

Bhaskar Kataria, Hammas Bin Tanveer, Rishab Nithyanand, and Rachee Singh. What Obstructed Skies Teach Us About Satellite Internet. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 7:1-7:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kataria_et_al:OASIcs.NINeS.2026.7,
  author =	{Kataria, Bhaskar and Tanveer, Hammas Bin and Nithyanand, Rishab and Singh, Rachee},
  title =	{{What Obstructed Skies Teach Us About Satellite Internet}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{7:1--7:25},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-414-7},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{139},
  editor =	{Argyraki, Katerina and Panda, Aurojit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NINeS.2026.7},
  URN =		{urn:nbn:de:0030-drops-255923},
  doi =		{10.4230/OASIcs.NINeS.2026.7},
  annote =	{Keywords: Satellite Internet, Starlink, Network Measurement, LEO Satellites, Obstructions}
}
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