119 Search Results for "Even, Guy"

Document
DOI: 10.4230/LIPIcs.ITC.2026.10
When Does Quantum Differential Privacy Compose?

Authors: Daniel Alabi and Theshani Nuradha

Published in: LIPIcs, Volume 385, 7th Conference on Information-Theoretic Cryptography (ITC 2026)

Abstract
Composition is a cornerstone of classical differential privacy, enabling strong end-to-end guarantees for complex algorithms through composition theorems (e.g., basic and advanced). In the quantum setting, however, privacy is defined operationally against arbitrary measurements, and classical composition arguments based on scalar privacy-loss random variables no longer apply. As a result, it has remained unclear when meaningful composition guarantees can be obtained for quantum differential privacy (QDP). In this work, we clarify both the limitations and possibilities of composition in the quantum setting. We first show that classical-style composition fails in full generality for POVM-based approximate QDP: even quantum channels that are individually perfectly private can completely lose privacy when combined through correlated joint implementations. We then identify a setting in which clean composition guarantees can be restored. For tensor-product channels acting on product neighboring inputs, we introduce a quantum moments accountant based on an operator-valued notion of privacy loss and a matrix moment-generating function. Although the resulting Rényi-type divergence does not satisfy a data-processing inequality, we prove that controlling its moments suffices to bound measured Rényi divergence, yielding operational privacy guarantees against arbitrary measurements. This leads to advanced-composition-style bounds with the same leading-order behavior as in the classical theory. Our results demonstrate that meaningful composition theorems for quantum differential privacy require carefully articulated structural assumptions on channels, inputs, and adversarial measurements, and provide a principled framework for understanding which classical ideas do and do not extend to the quantum setting.
Cite as

Daniel Alabi and Theshani Nuradha. When Does Quantum Differential Privacy Compose?. In 7th Conference on Information-Theoretic Cryptography (ITC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 385, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alabi_et_al:LIPIcs.ITC.2026.10,
  author =	{Alabi, Daniel and Nuradha, Theshani},
  title =	{{When Does Quantum Differential Privacy Compose?}},
  booktitle =	{7th Conference on Information-Theoretic Cryptography (ITC 2026)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-426-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{385},
  editor =	{Dodis, Yevgeniy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2026.10},
  URN =		{urn:nbn:de:0030-drops-271036},
  doi =		{10.4230/LIPIcs.ITC.2026.10},
  annote =	{Keywords: Quantum Information, Differential Privacy}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.8
General Multiplicative Spanners in Practice

Authors: Fritz Bökler, Markus Chimani, and Henning Jasper

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

Abstract
Given an undirected graph G with edge weights and lengths, a minimum α-spanner is a least-weight subgraph H ⊆ G that preserves distances w.r.t. the lengths between all node pairs up to a factor of α. Literature often takes the simplifying assumption of a single (coupled) edge function for weights and lengths. For such instances, several exact and non-exact algorithms are known and have been thoroughly evaluated in practice. However, many practical instances have decoupled form, as their weights and lengths are generally independent. Due to the increased complexity, only few (and even fewer practical) algorithms are able to guarantee low-weight solutions. This prompts practitioners to force their naturally decoupled instances into a coupled format, forsaking any quality guarantee. We implement several exact, approximative and heuristic algorithms for decoupled α-spanners, and use algorithm engineering to speed them up in practice. Our hypothesis-driven experiments evaluate their performance w.r.t. solution quality and speed. Generally, many practical instances can indeed be solved exactly within reasonable time, while LP-based approximation algorithms are not worthwhile. We find that standard greedy algorithms often yield acceptable results, but there are also practical instances for which they yield arbitrarily poor solutions. Here, augmented greedy variations offer a good compromise between solution quality and speed.
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Fritz Bökler, Markus Chimani, and Henning Jasper. General Multiplicative Spanners in Practice. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bokler_et_al:LIPIcs.SEA.2026.8,
  author =	{B\"{o}kler, Fritz and Chimani, Markus and Jasper, Henning},
  title =	{{General Multiplicative Spanners in Practice}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{8:1--8:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.8},
  URN =		{urn:nbn:de:0030-drops-260120},
  doi =		{10.4230/LIPIcs.SEA.2026.8},
  annote =	{Keywords: Graph spanners, ILP, experimental study, algorithm engineering}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.21
An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem

Authors: Luke Hawranick, Matthew Williamson, Jacob Restanio, K. Subramani, and Cody Klingler

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

Abstract
In this paper, we perform an experimental study of approximation algorithms for the unweighted tree augmentation problem (UTAP). Our goal is to establish a baseline performance for several existing approximation algorithms on actual instances rather than worst-case instances. In particular, we are interested in whether the algorithms' performance in practical instances is consistent with their worst-case guarantee rankings. We are also interested in whether preprocessing times, implementation difficulties, and running times justify the use of an algorithm in practice. We profile and analyze three approximation algorithms from the literature against a simple randomized algorithm. The performance of each algorithm was evaluated using metrics for space usage, running time, and solution quality. We found that the simple randomized algorithm is very competitive with the approximation algorithms and that the algorithms do not necessarily rank according to their theoretical guarantees. The randomized algorithm is easier to implement and understand, using less space than any of the more sophisticated approximation algorithms.
Cite as

Luke Hawranick, Matthew Williamson, Jacob Restanio, K. Subramani, and Cody Klingler. An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hawranick_et_al:LIPIcs.SEA.2026.21,
  author =	{Hawranick, Luke and Williamson, Matthew and Restanio, Jacob and Subramani, K. and Klingler, Cody},
  title =	{{An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.21},
  URN =		{urn:nbn:de:0030-drops-260259},
  doi =		{10.4230/LIPIcs.SEA.2026.21},
  annote =	{Keywords: Graphs, Networks, Tree Augmentation, Approximation Algorithms, Empirical}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.3
Computing k-mers in Graphs

Authors: Jarno N. Alanko and Máximo Pérez-López

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

Abstract
We initiate the study of computational problems on k-mers (strings of length k) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct k-mers found on the walks of a graph. We establish that this is #P-hard, even on connected deterministic DAGs. However, in the class of deterministic Wheeler graphs (Gagie, Manzini, and Sirén, TCS 2017), we show that distinct k-mers of such a graph W = (V, E) can be counted using O(|W|k) or O(n⁴ log k) arithmetic operations, where n = |V|, m = |E| and |W| = n+m. The latter result uses a new generalization of the technique of prefix doubling to Wheeler graphs. To generalize our results beyond Wheeler graphs, we discuss ways to transform a graph into a Wheeler graph in a manner that preserves the k-mers. As an application of our k-mer counting algorithms, we construct a representation of the de Bruijn graph of the k-mers that occupies O(n_k + |W|k log(max_{1 ≤ 𝓁 ≤ k} n_𝓁) + σlog m) bits of space, where n_𝓁 is the number of distinct 𝓁-mers in the Wheeler graph, and σ is the size of the alphabet. We show how to construct it in the same time complexity. Given that the Wheeler graph can be exponentially smaller than the de Bruijn graph, for large k this provides a theoretical improvement over previous de Bruijn graph construction methods from graphs, which must spend Ω(k) time per k-mer in the graph.
Cite as

Jarno N. Alanko and Máximo Pérez-López. Computing k-mers in Graphs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alanko_et_al:LIPIcs.CPM.2026.3,
  author =	{Alanko, Jarno N. and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{Computing k-mers in Graphs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.3},
  URN =		{urn:nbn:de:0030-drops-259294},
  doi =		{10.4230/LIPIcs.CPM.2026.3},
  annote =	{Keywords: Wheeler graph, Wheeler language, de Bruijn graph, graph, k-mer, q-gram, DFA, #P-hard}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.9
QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes

Authors: Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski

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

Abstract
We present a quasipolynomial-time approximation scheme (QPTAS) for the Maximum Independent Set (MWIS) in graphs with a bounded number of pairwise vertex-disjoint and non-adjacent long induced cycles. More formally, for every fixed s and t, we show a QPTAS for MWIS in graphs that exclude sC_t as an induced minor. Combining this with known results, we obtain a QPTAS for the problem of finding a largest induced subgraph of bounded treewidth with given hereditary property definable in Counting Monadic Second Order Logic, in the same classes of graphs. This is a step towards a conjecture of Gartland and Lokshtanov which asserts that for any planar graph H, graphs that exclude H as an induced minor admit a polynomial-time algorithm for the latter problem. This conjecture is notoriously open and even its weaker variants are confirmed only for very restricted graphs H.
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Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski. QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonnet_et_al:LIPIcs.SWAT.2026.9,
  author =	{Bonnet, \'{E}douard and Czy\.{z}ewska, Jadwiga and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.9},
  URN =		{urn:nbn:de:0030-drops-260454},
  doi =		{10.4230/LIPIcs.SWAT.2026.9},
  annote =	{Keywords: independent set, long holes, QPTAS, induced subgraphs}
}
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.FORC.2026.10
Packing Compact Subgraphs with Applications to Districting

Authors: Ho-Lin Chen, Po-Yu Chou, Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu

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

Abstract
Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and that satisfy additional composition requirements, such as a minimum population/weight threshold or balanced weight types (e.g., political affiliations). We aim to maximize coverage by disjoint districts that meet these requirements. In this work, we present new results that substantially improve the previously known bounds on balanced star districts for planar and minor-free graphs [Prathamesh Dharangutte et al., 2025]. In particular, we improve the approximation factor from O(log n) to O(1) for packing balanced star districts using the exact same algorithm, but with a refined analysis. We also extend the results beyond planar graphs to minor-free graphs and an even broader family of graphs of bounded expansion. Additionally, we obtain an O(1) approximation for packing radius-k districts (with a constant k) in planar and apex-minor-free graphs. In order to get a (1+ε) approximation on the max coverage, we show that this can be achieved if we allow a slight relaxation of the balancedness parameters (by a factor that can be made arbitrarily close to 1), for bounded radius-k districts on planar and apex-minor-free graphs. We show that all of these results can also be obtained if we enforce a minimum weight threshold for each district as the composition requirement, rather than balancedness. We present various results on hardness and hardness of approximation for this variant, by graph and district types.
Cite as

Ho-Lin Chen, Po-Yu Chou, Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu. Packing Compact Subgraphs with Applications to Districting. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 10:1-10:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.FORC.2026.10,
  author =	{Chen, Ho-Lin and Chou, Po-Yu and Dharangutte, Prathamesh and Gao, Jie and Huang, Shang-En and Yu, Fang-Yi},
  title =	{{Packing Compact Subgraphs with Applications to Districting}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{10:1--10:25},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-259820},
  doi =		{10.4230/LIPIcs.FORC.2026.10},
  annote =	{Keywords: Approximation algorithms, algorithmic fairness}
}
Document
DOI: 10.4230/LIPIcs.FORC.2026.1
Computational Hardness of Private Coreset

Authors: Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, and Pasin Manurangsi

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

Abstract
We study the problem of differentially private (DP) computation of coreset for the k-means objective. For a given input set of points, a coreset is another set of points such that the k-means objective for any candidate solution is preserved up to a multiplicative (1 ± α) factor (and some additive factor). We prove the first computational lower bounds for this problem. Specifically, assuming the existence of one-way functions, we show that no polynomial-time (ε, 1/n^{ω(1)})-DP algorithm can compute a coreset for k-means in the 𝓁_∞-metric for some constant α > 0 (and some constant additive factor), even for k = 3. For k-means in the Euclidean metric, we show a similar result but only for α = Θ(1/d²), where d is the dimension.
Cite as

Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, and Pasin Manurangsi. Computational Hardness of Private Coreset. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghazi_et_al:LIPIcs.FORC.2026.1,
  author =	{Ghazi, Badih and Guzm\'{a}n, Crist\'{o}bal and Kamath, Pritish and Knop, Alexander and Kumar, Ravi and Manurangsi, Pasin},
  title =	{{Computational Hardness of Private Coreset}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{1:1--1:14},
  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.2026.1},
  URN =		{urn:nbn:de:0030-drops-259725},
  doi =		{10.4230/LIPIcs.FORC.2026.1},
  annote =	{Keywords: Differentially Private Clustering, Coreset, Cryptographic Hardness}
}
Document
DOI: 10.4230/LIPIcs.FORC.2026.22
Separating Oblivious and Adaptive Differential Privacy Under Continual Observation

Authors: Mark Bun, Marco Gaboardi, and Connor Wagaman

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

Abstract
We resolve an open question of Jain, Raskhodnikova, Sivakumar, and Smith (ICML 2023) by exhibiting a problem separating differential privacy under continual observation in the oblivious and adaptive settings. The continual observation (a.k.a. continual release) model formalizes privacy for streaming algorithms, where data is received over time and output is released at each time step. In the oblivious setting, privacy need only hold for data streams fixed in advance; in the adaptive setting, privacy is required even for streams that can be chosen adaptively based on the streaming algorithm’s output. We describe the first explicit separation between the oblivious and adaptive settings. The problem showing this separation is based on the correlated vector queries problem of Bun, Steinke, and Ullman (SODA 2017). Specifically, we present an (ε,0)-DP algorithm for the oblivious setting that remains accurate for exponentially many time steps in the dimension of the input. On the other hand, we show that every (ε,δ)-DP adaptive algorithm fails to be accurate after releasing output for only a constant number of time steps.
Cite as

Mark Bun, Marco Gaboardi, and Connor Wagaman. Separating Oblivious and Adaptive Differential Privacy Under Continual Observation. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 22:1-22:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bun_et_al:LIPIcs.FORC.2026.22,
  author =	{Bun, Mark and Gaboardi, Marco and Wagaman, Connor},
  title =	{{Separating Oblivious and Adaptive Differential Privacy Under Continual Observation}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{22:1--22:11},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-259959},
  doi =		{10.4230/LIPIcs.FORC.2026.22},
  annote =	{Keywords: differential privacy, continual observation, continual release, streaming algorithms, adaptive algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.1
Covering and Partitioning Complex Objects with Small Pieces

Authors: Anders Aamand, Mikkel Abrahamsen, Reilly Browne, Mayank Goswami, Prahlad Narasimhan Kasthurirangan, Linda Kleist, Joseph S. B. Mitchell, Valentin Polishchuk, and Jack Stade

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

Abstract
We study the problems of covering or partitioning a polygon P (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to write P as a union of small pieces, and in partitioning, we furthermore require the pieces to be pairwise interior-disjoint. We show that these problems are in fact equivalent: Optimum covers and partitions have the same number of pieces. For covering, a natural local search algorithm repeatedly attempts to replace k pieces from a candidate cover with k-1 pieces. In two dimensions and for sufficiently large k, we show that when no such swap is possible, the cover is a 1+ O(1/√k) approximation, hence obtaining the first PTAS for the problem. Prior to our work, the only known algorithm was a 13-approximation that only works for polygons without holes [Abrahamsen and Rasmussen, SODA 2025]. In contrast, in the three dimensional version of the problem, for a polyhedron P of complexity n, we show that it is NP-hard to approximate an optimal cover or partition to within a factor that is logarithmic in n, even if P is simple, i.e., has genus 0 and no holes.
Cite as

Anders Aamand, Mikkel Abrahamsen, Reilly Browne, Mayank Goswami, Prahlad Narasimhan Kasthurirangan, Linda Kleist, Joseph S. B. Mitchell, Valentin Polishchuk, and Jack Stade. Covering and Partitioning Complex Objects with Small Pieces. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 1:1-1:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{aamand_et_al:LIPIcs.SoCG.2026.1,
  author =	{Aamand, Anders and Abrahamsen, Mikkel and Browne, Reilly and Goswami, Mayank and Kasthurirangan, Prahlad Narasimhan and Kleist, Linda and Mitchell, Joseph S. B. and Polishchuk, Valentin and Stade, Jack},
  title =	{{Covering and Partitioning Complex Objects with Small Pieces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{1:1--1:16},
  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.2026.1},
  URN =		{urn:nbn:de:0030-drops-258077},
  doi =		{10.4230/LIPIcs.SoCG.2026.1},
  annote =	{Keywords: Covering, partitioning, polygon, small piece, PTAS}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.24
Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support

Authors: Reilly Browne and Hsien-Chih Chang

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

Abstract
Given an unweighted graph G, the minimum r-dominating set problem asks for a subset of vertices S of the smallest cardinality, such that every vertex in G is within radius r to some vertex in S. While the r-dominating set problem on planar graph admits PTAS from Baker’s shifting/layering technique when r is a constant, the problem becomes significantly harder when r can depend on n. In fact, under Exponential-Time Hypothesis, Fox-Epstein ηl [SODA 2019] observed that no efficient PTAS can exist for the unbounded r-dominating set problem on planar graphs. One may consider even harder weighted-variant known as the vertex-weighted metric r-dominating set, where edges are associated with lengths, and every vertex is associated with a positive-valued weight, and the goal is to compute an r-dominating set with minimum total weight. As a result, people resorted to bicriteria algorithms by allowing the returned solution to use radius-(1+ε)r balls instead, in addition to the total weight being a 1+ε approximation to the optimal value. We establish the first single-criteria polynomial-time O(1)-approximation algorithm for the vertex-weighted metric r-dominating set problem on planar graphs when r is part of the input, and can be arbitrarily large compared to n. Our new (single-criteria) O(1)-approximation algorithm uses the quasi-uniformity sampling technique of Chan et al. [SODA 2012] by bounding the shallow cell complexity of the (unbounded) radius-r ball system to be linear in n. To this end we have two technical innovations: 1) The discrete ball system on planar graphs are neither pseudodisks nor have well-defined boundaries for standard union-complexity arguments. We construct a support graph for arbitrary distance ball systems as contractions of Voronoi cells; the sparseness comes as a byproduct. 2) We present an assignment of each depth-(≥3) cell to a unique 3-tuple of ball centers. This allows us to use standard Clarkson-Shor techniques to reduce the counting to cells of depth exactly 3, which we prove to be size O(n) by a novel geometric argument based on our support being a Voronoi contraction.
Cite as

Reilly Browne and Hsien-Chih Chang. Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{browne_et_al:LIPIcs.SoCG.2026.24,
  author =	{Browne, Reilly and Chang, Hsien-Chih},
  title =	{{Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{24:1--24:17},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-258300},
  doi =		{10.4230/LIPIcs.SoCG.2026.24},
  annote =	{Keywords: Minimum dominating set, planar graphs, shallow cell complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.14
Improved Online Hitting Set Algorithms for Structured and Geometric Set Systems

Authors: Sujoy Bhore, Anupam Gupta, and Amit Kumar

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

Abstract
In the online hitting set problem, sets arrive over time, and the algorithm has to maintain a subset of elements that hit all the sets seen so far. Alon, Awerbuch, Azar, Buchbinder, and Naor (SICOMP 2009) gave an algorithm with competitive ratio O(log n log m) for the (general) online hitting set and set cover problems for m sets and n elements; this is known to be tight for efficient online algorithms. Given this barrier for general set systems, we ask: can we break this double-logarithmic phenomenon for online hitting set/set cover on structured and geometric set systems? We provide an O(log n log log n)-competitive algorithm for the weighted online hitting set problem on set systems with linear shallow-cell complexity, replacing the double-logarithmic factor in the general result by effectively a single logarithmic term. As a consequence of our results we obtain the first bounds for weighted online hitting set for natural geometric set families, thereby answering open questions regarding the gap between general and geometric weighted online hitting set problems.
Cite as

Sujoy Bhore, Anupam Gupta, and Amit Kumar. Improved Online Hitting Set Algorithms for Structured and Geometric Set Systems. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.14,
  author =	{Bhore, Sujoy and Gupta, Anupam and Kumar, Amit},
  title =	{{Improved Online Hitting Set Algorithms for Structured and Geometric Set Systems}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{14:1--14:14},
  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.2026.14},
  URN =		{urn:nbn:de:0030-drops-258206},
  doi =		{10.4230/LIPIcs.SoCG.2026.14},
  annote =	{Keywords: Hitting Set, Online Algorithms, Shallow-Cell Complexity, VC-Dimension}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.7
Nemesis, an Escape Game in Graphs

Authors: Pierre Bergé, Antoine Dailly, and Yan Gerard

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

Abstract
We define a new escape game in graphs that we call Nemesis. The game is played on a graph having a subset of vertices labeled as exits and the goal of one of the two players, called the fugitive, is to reach one of these exit vertices. The second player, i.e. the fugitive adversary, is called the Nemesis. Her goal is to trap the fugitive in a connected component which does not contain any exit. At each round of the game, the fugitive moves from one vertex to an adjacent vertex. Then the Nemesis deletes one edge anywhere in the graph. The game ends when either the fugitive reached an exit or when he is in a connected component that does not contain any exit. In trees and graphs of maximum degree bounded by 3, Nemesis can be solved in linear time. For arbitrary graphs, we show that Nemesis is PSPACE-complete, and that it is NP-hard on planar multigraphs. We extend our results to the related Cat Herding problem, proving its PSPACE-completeness.
Cite as

Pierre Bergé, Antoine Dailly, and Yan Gerard. Nemesis, an Escape Game in Graphs. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{berge_et_al:LIPIcs.FUN.2026.7,
  author =	{Berg\'{e}, Pierre and Dailly, Antoine and Gerard, Yan},
  title =	{{Nemesis, an Escape Game in Graphs}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{7:1--7:22},
  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.2026.7},
  URN =		{urn:nbn:de:0030-drops-257261},
  doi =		{10.4230/LIPIcs.FUN.2026.7},
  annote =	{Keywords: Graphs, Evasion and Pursuit Games, PSPACE-completeness, Quantified SAT, Canadian Traveler Problem, Cat Herding Problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.40
Maker-Maker Games of Rank 4 Are PSPACE-Complete

Authors: Florian Galliot and Jonas Sénizergues

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
The Maker-Maker convention of positional games is played on a hypergraph whose edges are interpreted as winning sets. Two players take turns picking a previously unpicked vertex, aiming at being first to pick all the vertices of some edge. Optimal play can only lead to a first player win or a draw, and deciding between the two is known to be PSPACE-complete even for 6-uniform hypergraphs. We establish PSPACE-completeness for hypergraphs of rank 4. As an intermediary, we use the recently introduced achievement positional games, a more general convention in which each player has their own winning sets (blue and red). We show that deciding whether the blue player has a winning strategy as the first player is PSPACE-complete even with blue edges of size 2 or 3 and pairwise disjoint red edges of size 2. The result for hypergraphs of rank 4 in the Maker-Maker convention follows as a simple corollary.
Cite as

Florian Galliot and Jonas Sénizergues. Maker-Maker Games of Rank 4 Are PSPACE-Complete. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{galliot_et_al:LIPIcs.STACS.2026.40,
  author =	{Galliot, Florian and S\'{e}nizergues, Jonas},
  title =	{{Maker-Maker Games of Rank 4 Are PSPACE-Complete}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.40},
  URN =		{urn:nbn:de:0030-drops-255298},
  doi =		{10.4230/LIPIcs.STACS.2026.40},
  annote =	{Keywords: Game theory, Positional games, Combinatorial games, Complexity, Hypergraphs}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.32
Mean-Payoff and Energy Discrete-Bidding Games

Authors: Guy Avni and Suman Sadhukhan

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
A bidding game is played on a graph as follows. A token is placed on an initial vertex and both players are allocated budgets. In each turn, the players simultaneously submit bids that do not exceed their available budgets, the higher bidder moves the token, and pays the bid to the lower bidder. We focus on discrete-bidding, which are motivated by practical applications and restrict the granularity of the players' bids, e.g, bids must be given in cents. We study, for the first time, discrete-bidding games with mean-payoff and energy objectives. In contrast, mean-payoff continuous-bidding games (i.e., no granularity restrictions) are understood and exhibit a rich mathematical structure. The threshold budget is a necessary and sufficient initial budget for winning an energy game or guaranteeing a target payoff in a mean-payoff game. We first establish existence of threshold budgets; a non-trivial property due to the concurrent moves of the players. Moreover, we identify the structure of the thresholds, which is key in obtaining compact strategies, and in turn, showing that finding threshold is in NP and coNP even in succinctly-represented games.
Cite as

Guy Avni and Suman Sadhukhan. Mean-Payoff and Energy Discrete-Bidding Games. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{avni_et_al:LIPIcs.CSL.2026.32,
  author =	{Avni, Guy and Sadhukhan, Suman},
  title =	{{Mean-Payoff and Energy Discrete-Bidding Games}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.32},
  URN =		{urn:nbn:de:0030-drops-254573},
  doi =		{10.4230/LIPIcs.CSL.2026.32},
  annote =	{Keywords: Bidding games, Discrete-bidding, Mean-payoff games, energy games}
}
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