47 Search Results for "Larsen, Kasper Green"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.102
Smoothed Analysis of Dynamic Graph Algorithms

Authors: Uri Meir and Ami Paz

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

Abstract
Recent years have seen significant progress in the study of dynamic graph algorithms, and most notably, the introduction of strong lower bound techniques for them (e.g., Henzinger, Krinninger, Nanongkai and Saranurak, STOC 2015; Larsen and Yu, FOCS 2023). As worst-case analysis (adversarial inputs) may lead to the necessity of high running times, a natural question arises: in which cases are high running times really necessary, and in which cases these inputs merely manifest unique pathological cases? Early attempts to tackle this question were made by Nikoletseas, Reif, Spirakis and Yung (ICALP 1995) and by Alberts and Henzinger (Algorithmica 1998), who considered models with very little adversarial control over the inputs, and showed fast algorithms exist for them. The question was then overlooked for decades, until Henzinger, Lincoln and Saha (SODA 2022) recently addressed uniformly random inputs, and presented algorithms and impossibility results for several subgraph counting problems. To tackle the above question more thoroughly, we employ smoothed analysis, a celebrated framework introduced by Spielman and Teng (J. ACM, 2004). An input is proposed by an adversary but then a noisy version of it is processed by the algorithm instead. This model of inputs is parameterized by the amount of adversarial control, and fully interpolates between worst-case inputs and a uniformly random input. Doing so, we extend impossibility results for some problems to the smoothed model with only a minor quantitative loss. That is, we show that partially-adversarial inputs suffice to impose high running times for certain problems. In contrast, we show that other problems become easy even with the slightest amount of noise. In addition, we study the interplay between the adversary and the noise, leading to three natural models of smoothed inputs, for which we show a hierarchy of increasing difficulty stretching between the average-case and the worst-case complexities.
Cite as

Uri Meir and Ami Paz. Smoothed Analysis of Dynamic Graph Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 102:1-102:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{meir_et_al:LIPIcs.ITCS.2026.102,
  author =	{Meir, Uri and Paz, Ami},
  title =	{{Smoothed Analysis of Dynamic Graph Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{102:1--102:20},
  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.2026.102},
  URN =		{urn:nbn:de:0030-drops-253896},
  doi =		{10.4230/LIPIcs.ITCS.2026.102},
  annote =	{Keywords: Dynamic graph algorithms, Smoothed analysis, Shortest paths}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.82
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)

Copy BibTex To Clipboard

@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
DOI: 10.4230/LIPIcs.ITCS.2026.76
Ideal Private Simultaneous Messages Schemes and Their Applications

Authors: Keitaro Hiwatashi and Reo Eriguchi

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

Abstract
Private Simultaneous Messages (PSM) is a minimal model for secure computation, where two parties, Alice and Bob, have private inputs x,y and a shared random string. Each of them sends a single message to an external party, Charlie, who can compute f(x,y) for a public function f but learns nothing else. The problem of narrowing the gap between upper and lower bounds on the communication complexity of PSM has been widely studied, but the gap still remains exponential. In this work, we study the communication complexity of PSM from a different perspective and introduce a special class of PSM, referred to as ideal PSM, in which each party’s message length attains the minimum, that is, their messages are taken from the same domain as inputs. We initiate a systematic study of ideal PSM with a complete characterization, several positive results, and applications. First, we provide a characterization of the class of functions that admit ideal PSM, based on permutation groups acting on the input domain. This characterization allows us to derive asymptotic upper bounds on the total number of such functions and a complete list for small domains. We also present several infinite families of functions of practical interest that admit ideal PSM. Interestingly, by simply restricting the input domains of these ideal PSM schemes, we can recover most of the existing PSM schemes that achieve the best known communication complexity in various computation models. As applications, we show that these ideal PSM schemes yield novel communication-efficient PSM schemes for functions with sparse or dense truth-tables and those with low-rank truth-tables. Furthermore, we obtain a PSM scheme for general functions that improves the constant factor in the dominant term of the best known communication complexity. An additional advantage is that our scheme simplifies the existing construction by avoiding the hierarchical design of internally invoking PSM schemes for smaller functions.
Cite as

Keitaro Hiwatashi and Reo Eriguchi. Ideal Private Simultaneous Messages Schemes and Their Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 76:1-76:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{hiwatashi_et_al:LIPIcs.ITCS.2026.76,
  author =	{Hiwatashi, Keitaro and Eriguchi, Reo},
  title =	{{Ideal Private Simultaneous Messages Schemes and Their Applications}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{76:1--76:23},
  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.2026.76},
  URN =		{urn:nbn:de:0030-drops-253633},
  doi =		{10.4230/LIPIcs.ITCS.2026.76},
  annote =	{Keywords: secure computation, private simultaneous messages, communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.22
Simplicial Covering Dimension of Extremal Concept Classes

Authors: Ari Blondal, Hamed Hatami, Pooya Hatami, Chavdar Lalov, and Sivan Tretiak

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

Abstract
Dimension theory is a branch of topology concerned with defining and analyzing dimensions of geometric and topological spaces in purely topological terms. In this work, we adapt the classical notion of topological dimension (Lebesgue covering) to binary concept classes. The topological space naturally associated with a concept class is its space of realizable distributions. The loss function and the class itself induce a simplicial structure on this space, with respect to which we define a simplicial covering dimension. We prove that for finite concept classes, this simplicial covering dimension exactly characterizes the list replicability number (equivalently, global stability) in PAC learning. This connection allows us to apply tools from classical dimension theory to compute the exact list replicability number of the broad family of extremal concept classes.
Cite as

Ari Blondal, Hamed Hatami, Pooya Hatami, Chavdar Lalov, and Sivan Tretiak. Simplicial Covering Dimension of Extremal Concept Classes. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 22:1-22:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{blondal_et_al:LIPIcs.ITCS.2026.22,
  author =	{Blondal, Ari and Hatami, Hamed and Hatami, Pooya and Lalov, Chavdar and Tretiak, Sivan},
  title =	{{Simplicial Covering Dimension of Extremal Concept Classes}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{22:1--22:24},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-253094},
  doi =		{10.4230/LIPIcs.ITCS.2026.22},
  annote =	{Keywords: PAC Learning, Extremal Concept Classes, Replicability, List Replicability, Topology, Geometry}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.71
Lower Bounds on FSS from Dynamic Data Structures

Authors: Niv Gilboa and Daniel Weber

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

Abstract
In Function Secret Sharing (FSS), a dealer with a given function f: {0,1}ⁿ → 𝔾 from n bits to a commutative group 𝔾 such that f is in a function class ℱ shares succinct keys with two properties. Evaluating each key separately on a common input x results in additive shares of f(x) and any subset of the keys does not provide information on f. Two-party FSS schemes which are reducible to One-way Functions (OWF) have applications in cryptography, complexity, and in practical data security systems. We establish a two-way transformation between a two-party FSS scheme for a function class ℱ, which is black-box reducible to an OWF, or even black-box reducible to a family of Pseudo-Random Functions (PRF) and a dynamic data structure that supports range queries on ℱ. A data structure of this type enables dynamically adding functions to a multiset of functions F ⊆ ℱ, and answering range queries on the output of F, i.e., returning ∑_{f ∈ F} f(x) for a query x. The data structures are defined in one of several models which abstract RAM. The correspondence together with known lower bounds on the update time and the query time in data structures leads to the first non-trivial lower bounds on FSS schemes which are black-box reducible to PRF. These lower bounds apply to FSS schemes with polynomial key size and include: - For ℱ^d_{box}, the class of all functions which assign a constant group element β ∈ 𝔾 to any input in a specified d-dimensional box and 0 to all other inputs: if the key sharing function, Gen, runs in time polynomial in n and the evaluation function is Eval then: - If d ≥ 2 and 𝔾 = ℤ₂ then Eval’s running time is Ω ((n^{3/2})/(log³ n)). - If d ≥ 2 and 𝔾 is cyclic such that log |𝔾| = (1 + ε) n then Eval’s running time is Ω ((n/(log n)) ²). - If d > 2 is a constant and further, Gen and Eval correspond to operations on data structures in the Oblivious Group Model (this includes all known FSS from OWF techniques), then the product of Eval’s time and the key size is Ω(n^{d-1}). - For ℱ_{mono}, the class of all monomials ax^b ∈ 𝔽_{2ⁿ}[X] such that b ≤ B, assuming n^{ω(1)} ≤ B ≤ 2^{n/4}: if Gen runs in polynomial time, then Eval’s running time is Ω ((n √{log B})/(log² n)).
Cite as

Niv Gilboa and Daniel Weber. Lower Bounds on FSS from Dynamic Data Structures. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 71:1-71:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{gilboa_et_al:LIPIcs.ITCS.2026.71,
  author =	{Gilboa, Niv and Weber, Daniel},
  title =	{{Lower Bounds on FSS from Dynamic Data Structures}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{71:1--71:22},
  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.2026.71},
  URN =		{urn:nbn:de:0030-drops-253585},
  doi =		{10.4230/LIPIcs.ITCS.2026.71},
  annote =	{Keywords: FSS, Data Structures, Lower Bounds, Black-Box Reductions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.87
Range Longest Increasing Subsequence and Its Relatives

Authors: Karthik C. S. and Saladi Rahul

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

Abstract
Longest increasing subsequence (LIS) is a classical textbook problem which is still actively studied in various computational models. In this work, we present a few results for the range longest increasing subsequence problem (Range-LIS) and its variants. The input to Range-LIS is a sequence 𝒮 of n real numbers and a collection 𝒬 of m query ranges and for each query in 𝒬, the goal is to report the LIS of the sequence 𝒮 restricted to that query. Our two main results are for the following generalizations of the Range-LIS problem: 2D Range Queries: In this variant of the Range-LIS problem, each query is a pair of ranges, one of indices and the other of values, and we provide a randomized algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k), where k is the cumulative length of the m output subsequences. This improves on the elementary Õ(mn) runtime algorithm when m = Ω(√n). Previously, the only known result breaking the quadratic barrier was of Tiskin [SODA'10] which could only handle 1D range queries (i.e., each query was a range of indices) and also just outputted the length of the LIS (instead of reporting the subsequence achieving that length). Subsequent to our paper, Gawrychowski, Gorbachev, and Kociumaka in a preprint have extended Tiskin’s approach to handle reporting 1D range queries in O(n(log n)³+m+k) time. Colored Sequences: In this variant of the Range-LIS problem, each element in 𝒮 is colored and for each query in 𝒬, the goal is to report a monochromatic LIS contained in the sequence 𝒮 restricted to that query. For 2D queries, we provide a randomized algorithm for this colored version with running time Õ(mn^{2/3}+ n^{5/3})+O(k). Moreover, for 1D queries, we provide an improved algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k). Thus, we again improve on the elementary Õ(mn) runtime algorithm. Additionally, we prove that assuming the well-known Combinatorial Boolean Matrix Multiplication Hypothesis, that the runtime for 1D queries is essentially tight for combinatorial algorithms. Our algorithms combine several tools such as dynamic programming (to precompute increasing subsequences with some desirable properties), geometric data structures (to efficiently compute the dynamic programming entries), random sampling (to capture elements which are part of the LIS), classification of query ranges into large LIS and small LIS, and classification of colors into light and heavy. We believe that our techniques will be of interest to tackle other variants of LIS problem and other range-searching problems.
Cite as

Karthik C. S. and Saladi Rahul. Range Longest Increasing Subsequence and Its Relatives. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 87:1-87:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{karthikc.s._et_al:LIPIcs.ITCS.2026.87,
  author =	{Karthik C. S. and Rahul, Saladi},
  title =	{{Range Longest Increasing Subsequence and Its Relatives}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{87:1--87:20},
  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.2026.87},
  URN =		{urn:nbn:de:0030-drops-253740},
  doi =		{10.4230/LIPIcs.ITCS.2026.87},
  annote =	{Keywords: Longest Increasing Subsequence, Range Query, Fine-Grained Complexity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.41
Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions

Authors: Yasushi Kawase, Bodhayan Roy, and Mohammad Azharuddin Sanpui

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

Abstract
This paper explores the fair allocation of indivisible items in a multidimensional setting, motivated by the need to address fairness in complex environments where agents assess bundles according to multiple criteria. Such multidimensional settings are not merely of theoretical interest but are central to many real-world applications. For example, cloud computing resources are evaluated based on multiple criteria such as CPU cores, memory, and network bandwidth. In such cases, traditional one-dimensional fairness notions fail to capture fairness across multiple attributes. To address these challenges, we study two relaxed variants of envy-freeness: weak simultaneously envy-free up to c goods (weak sEFc) and strong simultaneously envy-free up to c goods (strong sEFc), which accommodate the multidimensionality of agents’ preferences. Under the weak notion, for every pair of agents and for each dimension, any perceived envy can be eliminated by removing, if necessary, a different set of goods from the envied agent’s allocation. In contrast, the strong version requires selecting a single set of goods whose removal from the envied bundle simultaneously eliminates envy in every dimension. We provide upper and lower bounds on the relaxation parameter c that guarantee the existence of weak or strong sEFc allocations, where these bounds are independent of the total number of items. In addition, we present algorithms for checking whether a weak or strong sEFc allocation exists. Moreover, we establish NP-hardness results for checking the existence of weak sEF1 and strong sEF1 allocations.
Cite as

Yasushi Kawase, Bodhayan Roy, and Mohammad Azharuddin Sanpui. Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions. 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. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kawase_et_al:LIPIcs.FSTTCS.2025.41,
  author =	{Kawase, Yasushi and Roy, Bodhayan and Sanpui, Mohammad Azharuddin},
  title =	{{Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{41:1--41:19},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-251210},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.41},
  annote =	{Keywords: Fair allocation, Envy-free up to one good, Multi-dimensional criteria, Linear programming, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.54
Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems

Authors: Bingbing Hu and Adam Polak

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

Abstract
Most of the known tight lower bounds for dynamic problems are based on the Online Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and understood as some more popular hypotheses in fine-grained complexity. It would be desirable to base hardness of dynamic problems on a more believable hypothesis. We propose analogues of the OMv Hypothesis for variants of matrix multiplication that are known to be harder than Boolean product in the offline setting, namely: equality, dominance, min-witness, min-max, and bounded monotone min-plus products. These hypotheses are a priori weaker assumptions than the standard (Boolean) OMv Hypothesis and yet we show that they are actually equivalent to it. This establishes the first such fine-grained equivalence class for dynamic problems.
Cite as

Bingbing Hu and Adam Polak. Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{hu_et_al:LIPIcs.ESA.2025.54,
  author =	{Hu, Bingbing and Polak, Adam},
  title =	{{Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.54},
  URN =		{urn:nbn:de:0030-drops-245228},
  doi =		{10.4230/LIPIcs.ESA.2025.54},
  annote =	{Keywords: Fine-grained complexity, OMv hypothesis, reductions, equivalence class}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.33
Better Indexing for Rectangular Pattern Matching

Authors: Paweł Gawrychowski and Adam Górkiewicz

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

Abstract
We revisit the complexity of building, given a two-dimensional string of size n, an indexing structure that allows locating all k occurrences of a two-dimensional pattern of size m. While a structure of size 𝒪(n) with query time 𝒪(m+k) is known for this problem under the additional assumption that the pattern is a square [Giancarlo, SICOMP 1995], a popular belief was that for rectangular patterns one cannot achieve such (or even similar) bounds, due to a lower bound for a certain natural class of approaches [Giancarlo, WADS 1993]. We show that, in fact, it is possible to construct a very simple structure of size 𝒪(nlog n) that supports such queries for any rectangular pattern in 𝒪(m+klog^{ε}n) time, for any ε > 0.
Cite as

Paweł Gawrychowski and Adam Górkiewicz. Better Indexing for Rectangular Pattern Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 33:1-33:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{gawrychowski_et_al:LIPIcs.ESA.2025.33,
  author =	{Gawrychowski, Pawe{\l} and G\'{o}rkiewicz, Adam},
  title =	{{Better Indexing for Rectangular Pattern Matching}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{33:1--33:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.33},
  URN =		{urn:nbn:de:0030-drops-245011},
  doi =		{10.4230/LIPIcs.ESA.2025.33},
  annote =	{Keywords: 2D strings, pattern matching, string indexing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.5
External-Memory Priority Queues with Optimal Insertions

Authors: Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning

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

Abstract
We present an external-memory priority queue structure supporting Insert and DeleteMin with amortized 𝒪(1) and 𝒪(lg N) comparisons, respectively, and amortized 𝒪(1/B) and 𝒪(1/B log_{M/B} N/B) I/Os, respectively. Here, M is the size of the internal memory, B is the block size of I/Os between internal and external memory, and N is the number of elements in the priority queue just before an operation is performed. Previous external-memory priority queues required amortized 𝒪(lg N) comparisons and 𝒪(1/B log_{M/B} N/B) I/Os for both Insert and DeleteMin. The construction requires the minimal assumption M ≥ 2B.
Cite as

Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning. External-Memory Priority Queues with Optimal Insertions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{brodal_et_al:LIPIcs.ESA.2025.5,
  author =	{Brodal, Gerth St{\o}lting and Goodrich, Michael T. and Iacono, John and Lo, Jared and Meyer, Ulrich and Pagan, Victor and Sitchinava, Nodari and Svenning, Rolf},
  title =	{{External-Memory Priority Queues with Optimal Insertions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.5},
  URN =		{urn:nbn:de:0030-drops-244734},
  doi =		{10.4230/LIPIcs.ESA.2025.5},
  annote =	{Keywords: priority queues, external memory, cache aware, amortized complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.44
Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity

Authors: Koustav Bhanja and Asaf Petruschka

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

Abstract
We present a compact labeling scheme for determining whether a designated set of terminals in a graph remains connected after any f (or less) vertex failures occur. An f-FT Steiner connectivity labeling scheme for an n-vertex graph G = (V,E) with terminal set U ⊆ V provides labels to the vertices of G, such that given only the labels of any subset F ⊆ V with |F| ≤ f, one can determine if U remains connected in G-F. The main complexity measure is the maximum label length. The special case U = V of global connectivity has been recently studied by Jiang, Parter, and Petruschka [Yonggang Jiang et al., 2025], who provided labels of n^{1-1/f} ⋅ poly(f,log n) bits. This is near-optimal (up to poly(f,log n) factors) by a lower bound of Long, Pettie and Saranurak [Yaowei Long et al., 2025]. Our scheme achieves labels of |U|^{1-1/f} ⋅ poly(f, log n) for general U ⊆ V, which is near-optimal for any given size |U| of the terminal set. To handle terminal sets, our approach differs from [Yonggang Jiang et al., 2025]. We use a well-structured Steiner tree for U produced by a decomposition theorem of Duan and Pettie [Ran Duan and Seth Pettie, 2020], and bypass the need for Nagamochi-Ibaraki sparsification [Hiroshi Nagamochi and Toshihide Ibaraki, 1992].
Cite as

Koustav Bhanja and Asaf Petruschka. Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 44:1-44:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bhanja_et_al:LIPIcs.ESA.2025.44,
  author =	{Bhanja, Koustav and Petruschka, Asaf},
  title =	{{Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{44:1--44:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.44},
  URN =		{urn:nbn:de:0030-drops-245123},
  doi =		{10.4230/LIPIcs.ESA.2025.44},
  annote =	{Keywords: Fault Tolerance, Labeling Schemes, Steiner Connectivity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.42
(Multivariate) k-SUM as Barrier to Succinct Computation

Authors: Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel

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

Abstract
How does the time complexity of a problem change when the input is given succinctly rather than explicitly? We study this question for several geometric problems defined on a set X of N points in ℤ^d. As succinct representation, we choose a sumset (or Minkowski sum) representation: Instead of receiving X explicitly, we are given sets A,B of n points that define X as A+B = {a+b∣ a ∈ A,b ∈ B}. We investigate the fine-grained complexity of this succinct version for several Õ(N)-time computable geometric primitives. Remarkably, we can tie their complexity tightly to the complexity of corresponding k-SUM problems. Specifically, we introduce as All-ints 3-SUM(n,n,k) the following multivariate, multi-output variant of 3-SUM: given sets A,B of size n and set C of size k, determine for all c ∈ C whether there are a ∈ A and b ∈ B with a+b = c. We obtain the following results: 1) Succinct closest L_∞-pair requires time N^{1-o(1)} under the 3-SUM hypothesis, while succinct furthest L_∞-pair can be solved in time Õ(n). 2) Succinct bichromatic closest L_∞-Pair requires time N^{1-o(1)} iff the 4-SUM hypothesis holds. 3) The following problems are fine-grained equivalent to All-ints 3-SUM(n,n,k): succinct skyline computation in 2D with output size k and succinct batched orthogonal range search with k given ranges. This establishes conditionally tight Õ(min{nk, N})-time algorithms for these problems. We obtain further connections with All-ints 3-SUM(n,n,k) for succinctly computing independent sets in unit interval graphs. Thus, (Multivariate) k-SUM problems precisely capture the barrier for enabling sumset-succinct computation for various geometric primitives.
Cite as

Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel. (Multivariate) k-SUM as Barrier to Succinct Computation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{gokaj_et_al:LIPIcs.ESA.2025.42,
  author =	{Gokaj, Geri and K\"{u}nnemann, Marvin and Storandt, Sabine and Truschel, Carina},
  title =	{{(Multivariate) k-SUM as Barrier to Succinct Computation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{42:1--42:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.42},
  URN =		{urn:nbn:de:0030-drops-245101},
  doi =		{10.4230/LIPIcs.ESA.2025.42},
  annote =	{Keywords: Fine-grained complexity theory, sumsets, additive combinatorics, succinct inputs, computational geometry}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.57
List-Recovery of Random Linear Codes over Small Fields

Authors: Dean Doron, Jonathan Mosheiff, Nicolas Resch, and João Ribeiro

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

Abstract
We study list-recoverability of random linear codes over small fields, both from errors and from erasures. We consider codes of rate ε-close to capacity, and aim to bound the dependence of the output list size L on ε, the input list size 𝓁, and the alphabet size q. Prior to our work, the best upper bound was L = q^O(𝓁/ε) (Zyablov and Pinsker, Prob. Per. Inf. 1981). Previous work has identified cases in which linear codes provably perform worse than non-linear codes with respect to list-recovery. While there exist non-linear codes that achieve L = O(𝓁/ε), we know that L ≥ 𝓁^Ω(1/ε) is necessary for list recovery from erasures over fields of small characteristic, and for list recovery from errors over large alphabets. We show that in other relevant regimes there is no significant price to pay for linearity, in the sense that we get the correct dependence on the gap-to-capacity ε and go beyond the Zyablov-Pinsker bound for the first time. Specifically, when q is constant and ε approaches zero, - For list-recovery from erasures over prime fields, we show that L ≤ C₁/ε. By prior work, such a result cannot be obtained for low-characteristic fields. - For list-recovery from errors over arbitrary fields, we prove that L ≤ C₂/ε. Above, C₁ and C₂ depend on the decoding radius, input list size, and field size. We provide concrete bounds on the constants above, and the upper bounds on L improve upon the Zyablov-Pinsker bound whenever q ≤ 2^{(1/ε)^c} for some small universal constant c > 0.
Cite as

Dean Doron, Jonathan Mosheiff, Nicolas Resch, and João Ribeiro. List-Recovery of Random Linear Codes over Small Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.57,
  author =	{Doron, Dean and Mosheiff, Jonathan and Resch, Nicolas and Ribeiro, Jo\~{a}o},
  title =	{{List-Recovery of Random Linear Codes over Small Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{57:1--57:18},
  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.2025.57},
  URN =		{urn:nbn:de:0030-drops-244239},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.57},
  annote =	{Keywords: List recovery, random linear codes}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.53
Near-Optimal List-Recovery of Linear Code Families

Authors: Ray Li and Nikhil Shagrithaya

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

Abstract
We prove several results on linear codes achieving list-recovery capacity. We show that random linear codes achieve list-recovery capacity with constant output list size (independent of the alphabet size and length). That is, over alphabets of size at least 𝓁^Ω(1/ε), random linear codes of rate R are (1-R-ε, 𝓁, (𝓁/ε)^O(𝓁/ε))-list-recoverable for all R ∈ (0,1) and 𝓁. Together with a result of Levi, Mosheiff, and Shagrithaya, this implies that randomly punctured Reed-Solomon codes also achieve list-recovery capacity. We also prove that our output list size is near-optimal among all linear codes: all (1-R-ε, 𝓁, L)-list-recoverable linear codes must have L ≥ 𝓁^{Ω(R/ε)}. Our simple upper bound combines the Zyablov-Pinsker argument with recent bounds from Kopparty, Ron-Zewi, Saraf, Wootters, and Tamo on the maximum intersection of a "list-recovery ball" and a low-dimensional subspace with large distance. Our lower bound is inspired by a recent lower bound of Chen and Zhang.
Cite as

Ray Li and Nikhil Shagrithaya. Near-Optimal List-Recovery of Linear Code Families. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{li_et_al:LIPIcs.APPROX/RANDOM.2025.53,
  author =	{Li, Ray and Shagrithaya, Nikhil},
  title =	{{Near-Optimal List-Recovery of Linear Code Families}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.53},
  URN =		{urn:nbn:de:0030-drops-244199},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.53},
  annote =	{Keywords: Error-Correcting Codes, Randomness, List-Recovery, Reed-Solomon Codes, Random Linear Codes}
}
  • Refine by Type
  • 47 Document/PDF
  • 30 Document/HTML

  • Refine by Publication Year
  • 6 2026
  • 24 2025
  • 5 2024
  • 2 2023
  • 2 2022
  • Show More...

  • Refine by Author
  • 17 Larsen, Kasper Green
  • 4 Grønlund, Allan
  • 2 Afshani, Peyman
  • 2 Bille, Philip
  • 2 Bringmann, Karl
  • Show More...

  • Refine by Series/Journal
  • 46 LIPIcs
  • 1 OASIcs

  • Refine by Classification
  • 8 Theory of computation → Data structures design and analysis
  • 7 Theory of computation → Computational geometry
  • 4 Theory of computation
  • 3 Theory of computation → Pattern matching
  • 3 Theory of computation → Random projections and metric embeddings
  • Show More...

  • Refine by Keyword
  • 3 clustering
  • 2 Clustering
  • 2 Computational Geometry
  • 2 Data Structures
  • 2 Fine-Grained Complexity
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact