7 Search Results for "Yasuda, Taisuke"

Document
DOI: 10.4230/LIPIcs.STACS.2026.69
Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time

Authors: Etienne Objois and Adrian Vladu

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

Abstract
We provide the first nearly-linear time algorithm for approximating 𝓁_{q → p}-norms of non-negative matrices, for q ≥ p ≥ 1. Our algorithm returns a (1-ε)-approximation to the matrix norm in time Õ(1/(q ε) ⋅ nnz(A)), where A is the input matrix, and improves upon the previous state of the art, which either proved convergence only in the limit [Boyd '74], or had very high polynomial running times [Bhaskara-Vijayraghavan, SODA '11]. Our algorithm is extremely simple, and is largely inspired from the coordinate-scaling approach used for positive linear program solvers. Our algorithm can readily be used in the [Englert-Räcke, FOCS '09] to improve the running time of constructing O(log n)-competitive 𝓁_p-oblivious routings.
Cite as

Etienne Objois and Adrian Vladu. Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 69:1-69:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{objois_et_al:LIPIcs.STACS.2026.69,
  author =	{Objois, Etienne and Vladu, Adrian},
  title =	{{Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{69:1--69:19},
  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.2026.69},
  URN =		{urn:nbn:de:0030-drops-255585},
  doi =		{10.4230/LIPIcs.STACS.2026.69},
  annote =	{Keywords: matrix norm, Perron-Frobenius theory, oblivious routings, input-sparsity time, lp norm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.58
Streaming Diameter of High-Dimensional Points

Authors: Magnús M. Halldórsson, Nicolaos Matsakis, and Pavel Veselý

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

Abstract
We improve the space bound for streaming approximation of Diameter but also of Farthest Neighbor queries, Minimum Enclosing Ball and its Coreset, in high-dimensional Euclidean spaces. In particular, our deterministic streaming algorithms store 𝒪(ε^{-2}log(1/(ε))) points. This improves by a factor of ε^{-1} the previous space bound of Agarwal and Sharathkumar (SODA 2010), while retaining the state-of-the-art approximation guarantees, such as √2+ε for Diameter or Farthest Neighbor queries, and also offering a simpler and more complete argument. Moreover, we show that storing Ω(ε^{-1}) points is necessary for a streaming (√2+ε)-approximation of Farthest Pair and Farthest Neighbor queries.
Cite as

Magnús M. Halldórsson, Nicolaos Matsakis, and Pavel Veselý. Streaming Diameter of High-Dimensional Points. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 58:1-58:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{halldorsson_et_al:LIPIcs.ESA.2025.58,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Matsakis, Nicolaos and Vesel\'{y}, Pavel},
  title =	{{Streaming Diameter of High-Dimensional Points}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{58:1--58:10},
  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.2025.58},
  URN =		{urn:nbn:de:0030-drops-245263},
  doi =		{10.4230/LIPIcs.ESA.2025.58},
  annote =	{Keywords: streaming algorithm, farthest pair, diameter, minimum enclosing ball, coreset}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.4
Streaming Algorithms for Network Design

Authors: Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian

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

Abstract
We consider the Survivable Network Design problem (SNDP) in the single-pass insertion-only streaming model. The input to SNDP is an edge-weighted graph G = (V, E) and an integer connectivity requirement r(uv) for each u, v ∈ V. The objective is to find a minimum-weight subgraph H ⊆ G such that, for every pair of vertices u, v ∈ V, u and v are r(uv)-edge/vertex-connected. Recent work by [Ce Jin et al., 2024] obtained approximation algorithms for edge-connectivity augmentation, and via that, also derived algorithms for edge-connectivity SNDP (EC-SNDP). In this work we consider vertex-connectivity setting (VC-SNDP) and obtain several results for it as well as improved results for EC-SNDP. - We provide a general framework for solving connectivity problems including SNDP and others in streaming; this is based on a connection to fault-tolerant spanners. For VC-SNDP we provide an O(tk)-approximation in Õ(k^{1-1/t}n^{1 + 1/t}) space, where k is the maximum connectivity requirement, assuming an exact algorithm at the end of the stream. Using a refined LP-based analysis, we provide an O(β t)-approximation where β is the integrality gap of the natural cut-based LP relaxation. These are the first approximation algorithms in the streaming model for VC-SNDP. When applied to the EC-SNDP, our framework provides an O(t)-approximation in Õ(k^{1/2-1/(2t)}n^{1 + 1/t} + kn) space, improving the O(t log k)-approximation of [Ce Jin et al., 2024] using Õ(kn^{1+1/t}) space; this also extends to element-connectivity SNDP. - We consider vertex connectivity-augmentation in the link-arrival model. The input is a k-vertex-connected spanning subgraph G, and additional weighted links L arrive in the stream; the goal is to store the min-weight set of links such that G ∪ L is (k+1)-vertex-connected. We obtain constant-factor approximations in near-linear space for k = 1, 2. Our result for k = 2 is based on using the SPQR tree, a novel application for this well-known representation of 2-connected graphs.
Cite as

Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian. Streaming Algorithms for Network Design. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chekuri_et_al:LIPIcs.APPROX/RANDOM.2025.4,
  author =	{Chekuri, Chandra and Jain, Rhea and Mahabadi, Sepideh and Vakilian, Ali},
  title =	{{Streaming Algorithms for Network Design}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{4:1--4:23},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-243709},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.4},
  annote =	{Keywords: Streaming Algorithms, Survivable Network Design, Fault-Tolerant Spanners}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.12
Relational Approximations for Subspace Primitives

Authors: Xiang Liu and Kasturi Varadarajan

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

Abstract
We explore fundamental geometric computations on point sets that are given to the algorithm implicitly. In particular, we are given a database which is a collection of tables with numerical values, and the geometric computation is to be performed on the join of the tables. Explicitly computing this join takes time exponential in the size of the tables. We are therefore interested in geometric problems that can be solved by algorithms whose running time is a polynomial in the size of the tables. Such relational algorithms are typically not able to explicitly compute the join. To avoid the NP-completeness bottleneck, researchers assume that the tables have a tractable combinatorial structure, like being acyclic. Even with this assumption, simple geometric computations turn out to be non-trivial and sometimes intractable. In this article, we study the problem of computing the maximum distance of a point in the join to a given subspace, and develop approximation algorithms for this NP-hard problem.
Cite as

Xiang Liu and Kasturi Varadarajan. Relational Approximations for Subspace Primitives. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.APPROX/RANDOM.2025.12,
  author =	{Liu, Xiang and Varadarajan, Kasturi},
  title =	{{Relational Approximations for Subspace Primitives}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{12:1--12:16},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-243781},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.12},
  annote =	{Keywords: relational algorithm, Euclidean distance, subspace approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.29
Guessing Efficiently for Constrained Subspace Approximation

Authors: Aditya Bhaskara, Sepideh Mahabadi, Madhusudhan Reddy Pittu, Ali Vakilian, and David P. Woodruff

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

Abstract
In this paper we study constrained subspace approximation problem. Given a set of n points {a₁,…,a_n} in ℝ^d, the goal of the subspace approximation problem is to find a k dimensional subspace that best approximates the input points. More precisely, for a given p ≥ 1, we aim to minimize the pth power of the 𝓁_p norm of the error vector (‖a₁-Pa₁‖,…,‖a_n-Pa_n‖), where P denotes the projection matrix onto the subspace and the norms are Euclidean. In constrained subspace approximation (CSA), we additionally have constraints on the projection matrix P. In its most general form, we require P to belong to a given subset 𝒮 that is described explicitly or implicitly. We introduce a general framework for constrained subspace approximation. Our approach, that we term coreset-guess-solve, yields either (1+ε)-multiplicative or ε-additive approximations for a variety of constraints. We show that it provides new algorithms for partition-constrained subspace approximation with applications to fair subspace approximation, k-means clustering, and projected non-negative matrix factorization, among others. Specifically, while we reconstruct the best known bounds for k-means clustering in Euclidean spaces, we improve the known results for the remainder of the problems.
Cite as

Aditya Bhaskara, Sepideh Mahabadi, Madhusudhan Reddy Pittu, Ali Vakilian, and David P. Woodruff. Guessing Efficiently for Constrained Subspace Approximation. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bhaskara_et_al:LIPIcs.ICALP.2025.29,
  author =	{Bhaskara, Aditya and Mahabadi, Sepideh and Pittu, Madhusudhan Reddy and Vakilian, Ali and Woodruff, David P.},
  title =	{{Guessing Efficiently for Constrained Subspace Approximation}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.29},
  URN =		{urn:nbn:de:0030-drops-234068},
  doi =		{10.4230/LIPIcs.ICALP.2025.29},
  annote =	{Keywords: parameterized complexity, low rank approximation, fairness, non-negative matrix factorization, clustering}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.77
Graph Spanners in the Message-Passing Model

Authors: Manuel Fernández V, David P. Woodruff, and Taisuke Yasuda

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Graph spanners are sparse subgraphs which approximately preserve all pairwise shortest-path distances in an input graph. The notion of approximation can be additive, multiplicative, or both, and many variants of this problem have been extensively studied. We study the problem of computing a graph spanner when the edges of the input graph are distributed across two or more sites in an arbitrary, possibly worst-case partition, and the goal is for the sites to minimize the communication used to output a spanner. We assume the message-passing model of communication, for which there is a point-to-point link between all pairs of sites as well as a coordinator who is responsible for producing the output. We stress that the subset of edges that each site has is not related to the network topology, which is fixed to be point-to-point. While this model has been extensively studied for related problems such as graph connectivity, it has not been systematically studied for graph spanners. We present the first tradeoffs for total communication versus the quality of the spanners computed, for two or more sites, as well as for additive and multiplicative notions of distortion. We show separations in the communication complexity when edges are allowed to occur on multiple sites, versus when each edge occurs on at most one site. We obtain nearly tight bounds (up to polylog factors) for the communication of additive 2-spanners in both the with and without duplication models, multiplicative (2k-1)-spanners in the with duplication model, and multiplicative 3 and 5-spanners in the without duplication model. Our lower bound for multiplicative 3-spanners employs biregular bipartite graphs rather than the usual Erdős girth conjecture graphs and may be of wider interest.
Cite as

Manuel Fernández V, David P. Woodruff, and Taisuke Yasuda. Graph Spanners in the Message-Passing Model. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 77:1-77:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{fernandezv_et_al:LIPIcs.ITCS.2020.77,
  author =	{Fern\'{a}ndez V, Manuel and Woodruff, David P. and Yasuda, Taisuke},
  title =	{{Graph Spanners in the Message-Passing Model}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{77:1--77:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.77},
  URN =		{urn:nbn:de:0030-drops-117620},
  doi =		{10.4230/LIPIcs.ITCS.2020.77},
  annote =	{Keywords: Graph spanners, Message-passing model, Communication complexity}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.1
The Query Complexity of Mastermind with l_p Distances

Authors: Manuel Fernández V, David P. Woodruff, and Taisuke Yasuda

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
Consider a variant of the Mastermind game in which queries are l_p distances, rather than the usual Hamming distance. That is, a codemaker chooses a hidden vector y in {-k,-k+1,...,k-1,k}^n and answers to queries of the form ||y-x||_p where x in {-k,-k+1,...,k-1,k}^n. The goal is to minimize the number of queries made in order to correctly guess y. In this work, we show an upper bound of O(min{n,(n log k)/(log n)}) queries for any real 1<=p<infty and O(n) queries for p=infty. To prove this result, we in fact develop a nonadaptive polynomial time algorithm that works for a natural class of separable distance measures, i.e., coordinate-wise sums of functions of the absolute value. We also show matching lower bounds up to constant factors, even for adaptive algorithms for the approximation version of the problem, in which the problem is to output y' such that ||y'-y||_p <= R for any R <= k^{1-epsilon}n^{1/p} for constant epsilon>0. Thus, essentially any approximation of this problem is as hard as finding the hidden vector exactly, up to constant factors. Finally, we show that for the noisy version of the problem, i.e., the setting when the codemaker answers queries with any q = (1 +/- epsilon)||y-x||_p, there is no query efficient algorithm.
Cite as

Manuel Fernández V, David P. Woodruff, and Taisuke Yasuda. The Query Complexity of Mastermind with l_p Distances. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 1:1-1:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{fernandezv_et_al:LIPIcs.APPROX-RANDOM.2019.1,
  author =	{Fern\'{a}ndez V, Manuel and Woodruff, David P. and Yasuda, Taisuke},
  title =	{{The Query Complexity of Mastermind with l\underlinep Distances}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{1:1--1:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.1},
  URN =		{urn:nbn:de:0030-drops-112165},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.1},
  annote =	{Keywords: Mastermind, Query Complexity, l\underlinep Distance}
}
  • Refine by Type
  • 7 Document/PDF
  • 5 Document/HTML

  • Refine by Publication Year
  • 1 2026
  • 4 2025
  • 1 2020
  • 1 2019

  • Refine by Author
  • 3 Woodruff, David P.
  • 2 Fernández V, Manuel
  • 2 Mahabadi, Sepideh
  • 2 Vakilian, Ali
  • 2 Yasuda, Taisuke
  • Show More...

  • Refine by Series/Journal
  • 7 LIPIcs

  • Refine by Classification
  • 2 Theory of computation → Routing and network design problems
  • 2 Theory of computation → Streaming, sublinear and near linear time algorithms
  • 1 Mathematics of computing → Combinatorics
  • 1 Mathematics of computing → Graph algorithms
  • 1 Theory of computation → Communication complexity
  • Show More...

  • Refine by Keyword
  • 1 Communication complexity
  • 1 Euclidean distance
  • 1 Fault-Tolerant Spanners
  • 1 Graph spanners
  • 1 Mastermind
  • 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