5 Search Results for "White, David"


Document
Multivariate to Bivariate Reduction for Noncommutative Polynomial Factorization

Authors: Vikraman Arvind and Pushkar S. Joglekar

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
Based on a theorem of Bergman [Cohn, 2006] we show that multivariate noncommutative polynomial factorization is deterministic polynomial-time reducible to the factorization of bivariate noncommutative polynomials. More precisely, we show the following: 1) In the white-box setting, given an n-variate noncommutative polynomial f ∈ 𝔽⟨X⟩ over a field 𝔽 (either a finite field or the rationals) as an arithmetic circuit (or algebraic branching program), computing a complete factorization of f into irreducible factors is deterministic polynomial-time reducible to white-box factorization of a noncommutative bivariate polynomial g ∈ 𝔽⟨x,y⟩; the reduction transforms f into a circuit for g (resp. ABP for g), and given a complete factorization of g (namely, arithmetic circuits (resp. ABPs) for irreducible factors of g) the reduction recovers a complete factorization of f in polynomial time. We also obtain a similar deterministic polynomial-time reduction in the black-box setting. 2) Additionally, we show over the field of rationals that bivariate linear matrix factorization of 4× 4 matrices is at least as hard as factoring square-free integers. This indicates that reducing noncommutative polynomial factorization to linear matrix factorization (as done in [Vikraman Arvind and Pushkar S. Joglekar, 2022]) is unlikely to succeed over the field of rationals even in the bivariate case. In contrast, multivariate linear matrix factorization for 3×3 matrices over rationals is in polynomial time.

Cite as

Vikraman Arvind and Pushkar S. Joglekar. Multivariate to Bivariate Reduction for Noncommutative Polynomial Factorization. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{arvind_et_al:LIPIcs.MFCS.2023.14,
  author =	{Arvind, Vikraman and Joglekar, Pushkar S.},
  title =	{{Multivariate to Bivariate Reduction for Noncommutative Polynomial Factorization}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.14},
  URN =		{urn:nbn:de:0030-drops-185480},
  doi =		{10.4230/LIPIcs.MFCS.2023.14},
  annote =	{Keywords: Arithmetic circuits, algebraic branching programs, polynomial factorization, automata, noncommutative polynomial ring}
}
Document
Track A: Algorithms, Complexity and Games
Robust Communication-Optimal Distributed Clustering Algorithms

Authors: Pranjal Awasthi, Ainesh Bakshi, Maria-Florina Balcan, Colin White, and David P. Woodruff

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
In this work, we study the k-median and k-means clustering problems when the data is distributed across many servers and can contain outliers. While there has been a lot of work on these problems for worst-case instances, we focus on gaining a finer understanding through the lens of beyond worst-case analysis. Our main motivation is the following: for many applications such as clustering proteins by function or clustering communities in a social network, there is some unknown target clustering, and the hope is that running a k-median or k-means algorithm will produce clusterings which are close to matching the target clustering. Worst-case results can guarantee constant factor approximations to the optimal k-median or k-means objective value, but not closeness to the target clustering. Our first result is a distributed algorithm which returns a near-optimal clustering assuming a natural notion of stability, namely, approximation stability [Awasthi and Balcan, 2014], even when a constant fraction of the data are outliers. The communication complexity is O~(sk+z) where s is the number of machines, k is the number of clusters, and z is the number of outliers. Next, we show this amount of communication cannot be improved even in the setting when the input satisfies various non-worst-case assumptions. We give a matching Omega(sk+z) lower bound on the communication required both for approximating the optimal k-means or k-median cost up to any constant, and for returning a clustering that is close to the target clustering in Hamming distance. These lower bounds hold even when the data satisfies approximation stability or other common notions of stability, and the cluster sizes are balanced. Therefore, Omega(sk+z) is a communication bottleneck, even for real-world instances.

Cite as

Pranjal Awasthi, Ainesh Bakshi, Maria-Florina Balcan, Colin White, and David P. Woodruff. Robust Communication-Optimal Distributed Clustering Algorithms. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{awasthi_et_al:LIPIcs.ICALP.2019.18,
  author =	{Awasthi, Pranjal and Bakshi, Ainesh and Balcan, Maria-Florina and White, Colin and Woodruff, David P.},
  title =	{{Robust Communication-Optimal Distributed Clustering Algorithms}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.18},
  URN =		{urn:nbn:de:0030-drops-105942},
  doi =		{10.4230/LIPIcs.ICALP.2019.18},
  annote =	{Keywords: robust distributed clustering, communication complexity}
}
Document
Invited Talk
Optimizing Society? Ensuring Fairness in Automated Decision-Making (Invited Talk)

Authors: Sorelle Friedler

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)


Abstract
Algorithms are increasingly used to make high-stakes decisions about people; who goes to jail, what neighborhoods police deploy to, and who should be hired for a job. But if we want these decisions to be fair, this means we must take societal notions of fairness and express them using the language of math. What is a fair decision and how can it be guaranteed? In this talk, we'll discuss recent work from the new and growing field of Fairness, Accountability, and Transparency. We will examine technical definitions of fairness and non-discrimination that have been proposed and their societal counterparts. We'll also discuss methods for ensuring that algorithms are making decisions as desired, from methods to audit black-box algorithms to white-box interpretability techniques. This important field necessitates societally informed and mathematically rigorous work; we'll discuss open problems in this light.

Cite as

Sorelle Friedler. Optimizing Society? Ensuring Fairness in Automated Decision-Making (Invited Talk). In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{friedler:LIPIcs.SWAT.2018.2,
  author =	{Friedler, Sorelle},
  title =	{{Optimizing Society? Ensuring Fairness in Automated Decision-Making}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.2},
  URN =		{urn:nbn:de:0030-drops-88282},
  doi =		{10.4230/LIPIcs.SWAT.2018.2},
  annote =	{Keywords: algorithmic fairness}
}
Document
Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas

Authors: Rafael Oliveira, Amir Shpilka, and Ben Lee Volk

Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)


Abstract
In this paper we give subexponential size hitting sets for bounded depth multilinear arithmetic formulas. Using the known relation between black-box PIT and lower bounds we obtain lower bounds for these models. For depth-3 multilinear formulas, of size exp(n^delta), we give a hitting set of size exp(~O(n^(2/3 + 2*delta/3))). This implies a lower bound of exp(~Omega(n^(1/2))) for depth-3 multilinear formulas, for some explicit polynomial. For depth-4 multilinear formulas, of size exp(n^delta), we give a hitting set of size exp(~O(n^(2/3 + 4*delta/3)). This implies a lower bound of exp(~Omega(n^(1/4))) for depth-4 multilinear formulas, for some explicit polynomial. A regular formula consists of alternating layers of +,* gates, where all gates at layer i have the same fan-in. We give a hitting set of size (roughly) exp(n^(1-delta)), for regular depth-d multilinear formulas of size exp(n^delta), where delta = O(1/sqrt(5)^d)). This result implies a lower bound of roughly exp(~Omega(n^(1/sqrt(5)^d))) for such formulas. We note that better lower bounds are known for these models, but also that none of these bounds was achieved via construction of a hitting set. Moreover, no lower bound that implies such PIT results, even in the white-box model, is currently known. Our results are combinatorial in nature and rely on reducing the underlying formula, first to a depth-4 formula, and then to a read-once algebraic branching program (from depth-3 formulas we go straight to read-once algebraic branching programs).

Cite as

Rafael Oliveira, Amir Shpilka, and Ben Lee Volk. Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 304-322, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{oliveira_et_al:LIPIcs.CCC.2015.304,
  author =	{Oliveira, Rafael and Shpilka, Amir and Volk, Ben Lee},
  title =	{{Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{304--322},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{Zuckerman, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.304},
  URN =		{urn:nbn:de:0030-drops-50548},
  doi =		{10.4230/LIPIcs.CCC.2015.304},
  annote =	{Keywords: Arithmetic Circuits, Derandomization, Polynomial Identity Testing}
}
Document
Accessing Databases within Esterel

Authors: David White and Gerald Luettgen

Published in: Dagstuhl Seminar Proceedings, Volume 4491, Synchronous Programming - SYNCHRON'04 (2005)


Abstract
A current limitation of the Esterel language for reactive-systems design is its lack of support for accessing databases. This talk presents the results of a summer student project which investigated a way of integrating databases and Esterel by providing an API for database use inside Esterel. A case study, involving a warehouse storage system built using Lego Mindstorms robotics kits, demonstrates the utility of the API. This system employs an Esterel-programmed robot whose task it is to collect various items from a customer's order and assemble them in one place. To do so, the robot accesses customer-order data and floor-plan data stored in a database.

Cite as

David White and Gerald Luettgen. Accessing Databases within Esterel. In Synchronous Programming - SYNCHRON'04. Dagstuhl Seminar Proceedings, Volume 4491, pp. 1-21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


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@InProceedings{white_et_al:DagSemProc.04491.3,
  author =	{White, David and Luettgen, Gerald},
  title =	{{Accessing Databases within Esterel}},
  booktitle =	{Synchronous Programming - SYNCHRON'04},
  pages =	{1--21},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4491},
  editor =	{Stephen A. Edwards and Nicolas Halbwachs and Reinhard v. Hanxleden and Thomas Stauner},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04491.3},
  URN =		{urn:nbn:de:0030-drops-1619},
  doi =		{10.4230/DagSemProc.04491.3},
  annote =	{Keywords: database esterel lego mindstorms}
}
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