5 Search Results for "van der Hoeven, Joris"

Document
DOI: 10.4230/LIPIcs.IPEC.2025.27
Uniformity Within Parameterized Circuit Classes

Authors: Steef Hegeman, Jan Martens, and Alfons Laarman

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

Abstract
We study uniformity conditions for parameterized Boolean circuit families. Uniformity conditions require that the infinitely many circuits in a circuit family are in some sense easy to construct from one shared description. For shallow circuit families, logtime-uniformity is often desired but quite technical to prove. Despite that, proving it is often left as an exercise for the reader - even for recently introduced classes in parameterized circuit complexity, where uniformity conditions have not yet been explicitly studied. We formally define parameterized versions of linear-uniformity, logtime-uniformity, and FO-uniformity, and prove that these result in equivalent complexity classes when imposed on para-AC⁰ and para-AC^{0↑}. Overall, we provide a convenient way to verify uniformity for shallow parameterized circuit classes, and thereby substantiate claims of uniformity in the literature.
Cite as

Steef Hegeman, Jan Martens, and Alfons Laarman. Uniformity Within Parameterized Circuit Classes. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hegeman_et_al:LIPIcs.IPEC.2025.27,
  author =	{Hegeman, Steef and Martens, Jan and Laarman, Alfons},
  title =	{{Uniformity Within Parameterized Circuit Classes}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{27:1--27:16},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-251598},
  doi =		{10.4230/LIPIcs.IPEC.2025.27},
  annote =	{Keywords: Parameterized complexity, circuit complexity, uniformity, descriptive complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.89
A Simple Algorithm for Trimmed Multipoint Evaluation

Authors: Nick Fischer, Melvin Kallmayer, and Leo Wennmann

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

Abstract
Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an n-variate polynomial with bounded individual degree d and total degree D, the goal is to evaluate it on a natural class of input points. This problem arises as a key subroutine in recent algorithmic results [Dinur; SODA '21], [Dell, Haak, Kallmayer, Wennmann; SODA '25]. It is known that trimmed multipoint evaluation can be solved in near-linear time [van der Hoeven, Schost; AAECC '13] by a clever yet somewhat involved algorithm. We give a simple recursive algorithm that avoids heavy computer-algebraic machinery, and can be readily understood by researchers without specialized background.
Cite as

Nick Fischer, Melvin Kallmayer, and Leo Wennmann. A Simple Algorithm for Trimmed Multipoint Evaluation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 89:1-89:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.ESA.2025.89,
  author =	{Fischer, Nick and Kallmayer, Melvin and Wennmann, Leo},
  title =	{{A Simple Algorithm for Trimmed Multipoint Evaluation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{89:1--89:11},
  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.2025.89},
  URN =		{urn:nbn:de:0030-drops-245574},
  doi =		{10.4230/LIPIcs.ESA.2025.89},
  annote =	{Keywords: Algebraic Algorithms, Multipoint Evaluation, Interpolation, LU Decomposition}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.6
Vantage Point Selection Algorithms for Bottleneck Capacity Estimation

Authors: Vikrant Ashvinkumar, Rezaul Chowdhury, Jie Gao, Mayank Goswami, Joseph S. B. Mitchell, and Valentin Polishchuk

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph G = (V, E) whose edges E have unknown capacity values that are to be discovered. Probes from a vantage point, i.e, a vertex v ∈ V, along shortest paths from v to all other vertices, reveal bottleneck edge capacities along each path. Our goal is to select k vantage points from V that reveal the maximum number of bottleneck edge capacities. We consider both a non-adaptive setting where all k vantage points are selected before any bottleneck capacity is revealed, and an adaptive setting where each vantage point selection instantly reveals bottleneck capacities along all shortest paths starting from that point. In the non-adaptive setting, by considering a relaxed model where edge capacities are drawn from a random permutation (which still leaves the problem of maximizing the expected number of revealed edges NP-hard), we are able to give a 1-1/e approximate algorithm. In the adaptive setting we work with the least permissive model where edge capacities are arbitrarily fixed but unknown. We compare with the best solution for the particular input instance (i.e. by enumerating all choices of k tuples), and provide both lower bounds on instance optimal approximation algorithms and upper bounds for trees and planar graphs.
Cite as

Vikrant Ashvinkumar, Rezaul Chowdhury, Jie Gao, Mayank Goswami, Joseph S. B. Mitchell, and Valentin Polishchuk. Vantage Point Selection Algorithms for Bottleneck Capacity Estimation. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ashvinkumar_et_al:LIPIcs.WADS.2025.6,
  author =	{Ashvinkumar, Vikrant and Chowdhury, Rezaul and Gao, Jie and Goswami, Mayank and Mitchell, Joseph S. B. and Polishchuk, Valentin},
  title =	{{Vantage Point Selection Algorithms for Bottleneck Capacity Estimation}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.6},
  URN =		{urn:nbn:de:0030-drops-242376},
  doi =		{10.4230/LIPIcs.WADS.2025.6},
  annote =	{Keywords: Bottleneck capacity, Approximation algorithms, Instance optimality}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.131
Deterministic Complexity Analysis of Hermitian Eigenproblems

Authors: Aleksandros Sobczyk

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

Abstract
In this work we revisit the arithmetic and bit complexity of Hermitian eigenproblems. Recently, [BGVKS, FOCS 2020] proved that a (non-Hermitian) matrix A can be diagonalized with a randomized algorithm in O(n^{ω}log²(n/ε)) arithmetic operations, where ω≲ 2.371 is the square matrix multiplication exponent, and [Shah, SODA 2025] significantly improved the bit complexity for the Hermitian case. Our main goal is to obtain similar deterministic complexity bounds for various Hermitian eigenproblems. In the Real RAM model, we show that a Hermitian matrix can be diagonalized deterministically in O(n^{ω}log(n)+n²polylog(n/ε)) arithmetic operations, improving the classic deterministic Õ(n³) algorithms, and derandomizing the aforementioned state-of-the-art. The main technical step is a complete, detailed analysis of a well-known divide-and-conquer tridiagonal eigensolver of Gu and Eisenstat [GE95], when accelerated with the Fast Multipole Method, asserting that it can accurately diagonalize a symmetric tridiagonal matrix in nearly-O(n²) operations. In finite precision, we show that an algorithm by Schönhage [Sch72] to reduce a Hermitian matrix to tridiagonal form is stable in the floating point model, using O(log(n/ε)) bits of precision. This leads to a deterministic algorithm to compute all the eigenvalues of a Hermitian matrix in O(n^{ω}ℱ(log(n/ε)) + n²polylog(n/ε)) bit operations, where ℱ(b) ∈ Õ(b) is the bit complexity of a single floating point operation on b bits. This improves the best known Õ(n³) deterministic and O(n^{ω}log²(n/ε)ℱ(log(n/ε))) randomized complexities. We conclude with some other useful subroutines such as computing spectral gaps, condition numbers, and spectral projectors, and with some open problems.
Cite as

Aleksandros Sobczyk. Deterministic Complexity Analysis of Hermitian Eigenproblems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 131:1-131:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sobczyk:LIPIcs.ICALP.2025.131,
  author =	{Sobczyk, Aleksandros},
  title =	{{Deterministic Complexity Analysis of Hermitian Eigenproblems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{131:1--131:21},
  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.2025.131},
  URN =		{urn:nbn:de:0030-drops-235081},
  doi =		{10.4230/LIPIcs.ICALP.2025.131},
  annote =	{Keywords: Hermitian eigenproblem, eigenvalues, SVD, tridiagonal reduction, matrix multiplication time, diagonalization, bit complexity}
}
Document
DOI: 10.4230/DagSemProc.06271.10
GNU TeXmacs

Authors: Joris van der Hoeven

Published in: Dagstuhl Seminar Proceedings, Volume 6271, Challenges in Symbolic Computation Software (2006)

Abstract
GNU TeXmacs is a free scientific editing platform with special features for mathematicians. The editor can be used to produce documents with a professional typesetting quality (better than TeX/LaTeX) via a user-friendly front-end. The editor can be used as a front-end to several computer algebra systems and includes a lot of additional facilities, like a presentation mode, a technical picture editor, a typed linking tool, etc. The editor can be extended by users in several ways: using style files, plug-ins or via the Scheme extension language. Converters exist for LaTeX, Xhtml and MathML.
Cite as

Joris van der Hoeven. GNU TeXmacs. In Challenges in Symbolic Computation Software. Dagstuhl Seminar Proceedings, Volume 6271, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{vanderhoeven:DagSemProc.06271.10,
  author =	{van der Hoeven, Joris},
  title =	{{GNU TeXmacs}},
  booktitle =	{Challenges in Symbolic Computation Software},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06271.10},
  URN =		{urn:nbn:de:0030-drops-7672},
  doi =		{10.4230/DagSemProc.06271.10},
  annote =	{Keywords: Scientific text editor, Mathematics, Computer algebra system, Front-end}
}
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