Vincent Neiger

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ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation (2)
ISSAC '18: Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation (2)
ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation (2)
ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation (2)
ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation (2)
ISSAC '24: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation (2)
Advances in Cryptology – EUROCRYPT 2020 (1)
ISSAC '19: Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation (1)
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Computing Krylov iterates in the time of matrix multiplication
- Vincent Neiger
  LIP6, Sorbonne Université, CNRS, France
  ,
- Clément Pernet
  Grenoble INP - UGA, CNRS, France
  ,
- Gilles Villard
  LIP, CNRS, ENS de Lyon, Univ de Lyon, Inria, UCBL, France
ISSAC '24: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation•July 2024, pp 419-428• https://doi.org/10.1145/3666000.3669715

Krylov methods rely on iterated matrix-vector products Akuj for an n × n matrix A and vectors u1, …, um. The space spanned by all iterates Akuj admits a particular basis — the maximal Krylov basis — which consists of iterates of the first vector u1, Au1,...
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Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations
- Sriram Gopalakrishnan
  LIP6, Sorbonne Université, France and David R. Cheriton School of Computer Science, University of Waterloo, Canada
  ,
- Vincent Neiger
  LIP6, Sorbonne Université, France
  ,
- Mohab Safey El Din
  LIP6, Sorbonne Université, France
ISSAC '24: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation•July 2024, pp 400-409• https://doi.org/10.1145/3666000.3669713

Given polynomials g and f1, …, fp, all in <Formula format="inline"><TexMath><?TeX $\field [x_1,\dots,x_n]$?></TexMath><AltText>Math 1</AltText><File name="issac24-43-inline1" type="svg"/></Formula> for some field <Formula format="inline"><TexMath><?TeX $...
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Faster Modular Composition
- Vincent Neiger
  Sorbonne Université, Paris, France
  ,
- Bruno Salvy
  Inria, Lyon, France
  ,
- Éric Schost
  University of Waterloo, Waterloo, Canada
  ,
- Gilles Villard
  CNRS, Lyon, France
Journal of the ACM, Volume 71, Issue 2•April 2024, Article No.: 11, pp 1-79 • https://doi.org/10.1145/3638349
A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by n, the algorithm uses O(n^1.43) field operations, breaking through the 3/2 ...
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Beating binary powering for polynomial matrices
- Alin Bostan
  Inria, France
  ,
- Vincent Neiger
  Sorbonne Université, CNRS, LIP6, France
  ,
- Sergey Yurkevich
  University of Vienna, Austria and Inria, France
ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation•July 2023, pp 70-79• https://doi.org/10.1145/3597066.3597118

The Nth power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in N. When Fast Fourier Transform (FFT) is available, the resulting complexity is softly linear in N,...
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Refined F5 Algorithms for Ideals of Minors of Square Matrices
- Sriram Gopalakrishnan
  Sorbonne Université, France
  ,
- Vincent Neiger
  Sorbonne Université, France
  ,
- Mohab Safey El Din
  Sorbonne Université, France
ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation•July 2023, pp 270-279• https://doi.org/10.1145/3597066.3597077

We consider the problem of computing a grevlex Gröbner basis for the set Fr(M) of minors of size r of an n × n matrix M of generic linear forms over a field of characteristic zero or large enough. Such sets are not regular sequences; in fact, the ideal ⟨...
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Rank-Sensitive Computation of the Rank Profile of a Polynomial Matrix
- George Labahn
  University of Waterloo, Waterloo, Canada
  ,
- Vincent Neiger
  Sorbonne Université, CNRS, LIP6, Paris, France
  ,
- Thi Xuan Vu
  UiT, The Arctic University of Norway, Tromso, Norway
  ,
- Wei Zhou
  University of Waterloo, Waterloo, Canada
ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation•July 2022, pp 351-360• https://doi.org/10.1145/3476446.3535495

Consider a matrix F ε K [x]^mxn of univariate polynomials over a field K. We study the problem of computing the column rank profile of F. To this end we first give an algorithm which improves the minimal kernel basis algorithm of Zhou, Labahn, and ...
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Faster Change of Order Algorithm for Gröbner Bases under Shape and Stability Assumptions
- Jérémy Berthomieu
  Sorbonne Université, CNRS, LIP6, Paris, France
  ,
- Vincent Neiger
  Sorbonne Université, CNRS, LIP6, Paris, France
  ,
- Mohab Safey El Din
  Sorbonne Université, CNRS, LIP6, Paris, France
ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation•July 2022, pp 409-418• https://doi.org/10.1145/3476446.3535484

Solving zero-dimensional polynomial systems using Gröbner bases is usually done by, first, computing a Gröbner basis for the degree reverse lexicographic order, and next computing the lexicographic Gröbner basis with a change of order algorithm. ...
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Deterministic computation of the characteristic polynomial in the time of matrix multiplication
- Vincent Neiger
  Univ. Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France
  ,
- Clément Pernet
  Université Grenoble Alpes, Laboratoire Jean Kuntzmann, CNRS, UMR 5224, 700 avenue centrale, IMAG - CS 40700, 38058 Grenoble cedex 9, France
Journal of Complexity, Volume 67, Issue C•Dec 2021 • https://doi.org/10.1016/j.jco.2021.101572
Abstract
This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was ...
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Algorithms for Linearly Recurrent Sequences of Truncated Polynomials
- Seung Gyu Hyun
  University of Waterloo, Waterloo, ON, Canada
  ,
- Vincent Neiger
  University Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France
  ,
- Éric Schost
  University of Waterloo, Waterloo, ON, Canada
ISSAC '21: Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation•July 2021, pp 201-208• https://doi.org/10.1145/3452143.3465533

Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements are vectors ...
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A divide-and-conquer algorithm for computing gröbner bases of syzygies in finite dimension
- Simone Naldi
  Univ. Limoges, Limoges, France
  ,
- Vincent Neiger
  Univ. Limoges, Limoges, France
ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation•July 2020, pp 380-387• https://doi.org/10.1145/3373207.3404059

Let f₁, ..., f_m be elements in a quotient Rⁿ/N which has finite dimension as a K-vector space, where R = K[X₁, ..., X_r] and N is an R-submodule of Rⁿ. We address the problem of computing a Gröbner basis of the module of syzygies of (f₁, ..., f_m), that ...
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Generic bivariate multi-point evaluation, interpolation and modular composition with precomputation
- Vincent Neiger
  Univ. Limoges, Limoges, France
  ,
- Johan Rosenkilde
  Technical University of Denmark, Kgs. Lyngby, Denmark
  ,
- Grigory Solomatov
  Technical University of Denmark, Kgs. Lyngby, Denmark
ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation•July 2020, pp 388-395• https://doi.org/10.1145/3373207.3404032

Suppose K is a large enough field and P ⊂ K² is a fixed, generic set of points which is available for precomputation. We introduce a technique called reshaping which allows us to design quasi-linear algorithms for both: computing the evaluations of an ...
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An Algebraic Attack on Rank Metric Code-Based Cryptosystems
- Magali Bardet
  LITIS, University of Rouen Normandie, Mont-Saint-Aignan, France
  Inria, 2 rue Simone Iff, 75012, Paris, France
  ,
- Pierre Briaud
  Inria, 2 rue Simone Iff, 75012, Paris, France
  ,
- Maxime Bros
  Univ. Limoges, CNRS, XLIM, UMR 7252, 87000, Limoges, France
  ,
- Philippe Gaborit
  Univ. Limoges, CNRS, XLIM, UMR 7252, 87000, Limoges, France
  ,
- Vincent Neiger
  Univ. Limoges, CNRS, XLIM, UMR 7252, 87000, Limoges, France
  ,
- Olivier Ruatta
  Univ. Limoges, CNRS, XLIM, UMR 7252, 87000, Limoges, France
  ,
- Jean-Pierre Tillich
  Inria, 2 rue Simone Iff, 75012, Paris, France
Advances in Cryptology – EUROCRYPT 2020•May 2020, pp 64-93• https://doi.org/10.1007/978-3-030-45727-3_3
Abstract
The Rank metric decoding problem is the main problem considered in cryptography based on codes in the rank metric. Very efficient schemes based on this problem or quasi-cyclic versions of it have been proposed recently, such as those in the ...
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Fast computation of approximant bases in canonical form
- Claude-Pierre Jeannerod
  Univ Lyon, Inria, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR 5668, F-69007 Lyon, France
  ,
- Vincent Neiger
  Univ. Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France
  ,
- Gilles Villard
  Univ Lyon, CNRS, ENS de Lyon, Inria, Université Claude Bernard Lyon 1, LIP UMR 5668, F-69007 Lyon, France
Journal of Symbolic Computation, Volume 98, Issue C•May 2020, pp 192-224 • https://doi.org/10.1016/j.jsc.2019.07.011
Abstract
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix ...
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Block-Krylov techniques in the context of sparse-FGLM algorithms
- Seung Gyu Hyun
  Cheriton School of Computer Science, University of Waterloo, Canada
  ,
- Vincent Neiger
  Univ. Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France
  ,
- Hamid Rahkooy
  Cheriton School of Computer Science, University of Waterloo, Canada
  ,
- Éric Schost
  Cheriton School of Computer Science, University of Waterloo, Canada
Journal of Symbolic Computation, Volume 98, Issue C•May 2020, pp 163-191 • https://doi.org/10.1016/j.jsc.2019.07.010
Abstract
Consider a zero-dimensional ideal I in K [ X 1 , … , X n ]. Inspired by Faugère and Mou's Sparse FGLM algorithm, we use Krylov sequences based on multiplication matrices of I in order to compute a description of its zero set by means ...
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Implementations of Efficient Univariate Polynomial Matrix Algorithms and Application to Bivariate Resultants
- Seung Gyu Hyun
  University of Waterloo, Waterloo, ON, Canada
  ,
- Vincent Neiger
  Univ. Limoges, CNRS, XLIM, UMR7252, Limoges, France
  ,
- Éric Schost
  University of Waterloo, Waterloo, ON, Canada
ISSAC '19: Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation•July 2019, pp 235-242• https://doi.org/10.1145/3326229.3326272

Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of the practical ...
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Sparse FGLM using the block Wiedemann algorithm
ACM Communications in Computer Algebra, Volume 52, Issue 4•December 2018, pp 123-125 • https://doi.org/10.1145/3338637.3338641

Overview. Computing the Gröbner basis of an ideal with respect to a term ordering is an essential step in solving systems of polynomials; in what follows, we restrict our attention to systems with finitely many solutions. Certain term orderings, such as ...
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Two-Point Codes for the Generalized GK Curve
- Elise Barelli
  Inria Saclay and LIX, École Polytechnique, Palaiseau Cedex, France
  ,
- Peter Beelen
  Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark
  ,
- Mrinmoy Datta
  Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark
  ,
- Vincent Neiger
  Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark
  ,
- Johan Rosenkilde
  Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark
IEEE Transactions on Information Theory, Volume 64, Issue 9•September 2018, pp 6268-6276 • https://doi.org/10.1109/TIT.2017.2763165

We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the ...
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Certification of Minimal Approximant Bases
- Pascal Giorgi
  LIRMM, Université de Montpellier, CNRS, Montpellier, France
  ,
- Vincent Neiger
  Univ. Limoges, CNRS, XLIM, UMR 7252, Limoges, France
ISSAC '18: Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation•July 2018, pp 167-174• https://doi.org/10.1145/3208976.3208991

For a given computational problem, a certificate is a piece of data that one (the prover) attaches to the output with the aim of allowing efficient verification (by the verifier) that this output is correct. Here, we consider the minimal approximant ...
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Computing Popov and Hermite Forms of Rectangular Polynomial Matrices
- Vincent Neiger
  Univ. Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France
  ,
- Johan Rosenkilde
  Technical University of Denmark, Kgs. Lyngby, Denmark
  ,
- Grigory Solomatov
  Technical University of Denmark, Kgs. Lyngby, Denmark
ISSAC '18: Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation•July 2018, pp 295-302• https://doi.org/10.1145/3208976.3208988

We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are known. Here, we ...
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Computing Canonical Bases of Modules of Univariate Relations
- Vincent Neiger
  Technical University of Denmark, Kgs. Lyngby, Denmark
  ,
- Vu Thi Xuan
  Ecole Normale Superieure de Lyon, Lyon, France
ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation•July 2017, pp 357-364• https://doi.org/10.1145/3087604.3087656

We study the computation of canonical bases of sets of univariate relations (p₁,...,p_m) ∈ K[x]^m such that p₁ f₁ + ⋯ + p_m f_m = 0; here, the input elements f₁,...,f_m are from a quotient K[x]ⁿ/M, where M is a K[x]-module of rank n given by a basis M ∈ K[x]^{n ...}
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Summary Description

ACM Author-Izer is a unique service that enables ACM authors to generate and post links on both their homepage and institutional repository for visitors to download the definitive version of their articles from the ACM Digital Library at no charge.

Downloads from these sites are captured in official ACM statistics, improving the accuracy of usage and impact measurements. Consistently linking to definitive version of ACM articles should reduce user confusion over article versioning.

ACM Author-Izer also extends ACM’s reputation as an innovative “Green Path” publisher, making ACM one of the first publishers of scholarly works to offer this model to its authors.

To access ACM Author-Izer, authors need to establish a free ACM web account. Should authors change institutions or sites, they can utilize the new ACM service to disable old links and re-authorize new links for free downloads from a different site.

How ACM Author-Izer Works

Authors may post ACM Author-Izer links in their own bibliographies maintained on their website and their own institution’s repository. The links take visitors to your page directly to the definitive version of individual articles inside the ACM Digital Library to download these articles for free.

The Service can be applied to all the articles you have ever published with ACM.

Depending on your previous activities within the ACM DL, you may need to take up to three steps to use ACM Author-Izer.

For authors who do not have a free ACM Web Account:

Go to the ACM DL http://dl.acm.org/ and click SIGN UP. Once your account is established, proceed to next step.

For authors who have an ACM web account, but have not edited their ACM Author Profile page:

Sign in to your ACM web account and go to your Author Profile page. Click "Add personal information" and add photograph, homepage address, etc. Click ADD AUTHOR INFORMATION to submit change. Once you receive email notification that your changes were accepted, you may utilize ACM Author-izer.

For authors who have an account and have already edited their Profile Page:

Sign in to your ACM web account, go to your Author Profile page in the Digital Library, look for the ACM Author-izer link below each ACM published article, and begin the authorization process. If you have published many ACM articles, you may find a batch Authorization process useful. It is labeled: "Export as: ACM Author-Izer Service"

ACM Author-Izer also provides code snippets for authors to display download and citation statistics for each “authorized” article on their personal pages. Downloads from these pages are captured in official ACM statistics, improving the accuracy of usage and impact measurements. Consistently linking to the definitive version of ACM articles should reduce user confusion over article versioning.

Note: You still retain the right to post your author-prepared preprint versions on your home pages and in your institutional repositories with DOI pointers to the definitive version permanently maintained in the ACM Digital Library. But any download of your preprint versions will not be counted in ACM usage statistics. If you use these AUTHOR-IZER links instead, usage by visitors to your page will be recorded in the ACM Digital Library and displayed on your page.

FAQ

Q. What is ACM Author-Izer?
A. ACM Author-Izer is a unique, link-based, self-archiving service that enables ACM authors to generate and post links on either their home page or institutional repository for visitors to download the definitive version of their articles for free.
Q. What articles are eligible for ACM Author-Izer?
A. ACM Author-Izer can be applied to all the articles authors have ever published with ACM. It is also available to authors who will have articles published in ACM publications in the future.

Q. Are there any restrictions on authors to use this service?
A. No. An author does not need to subscribe to the ACM Digital Library nor even be a member of ACM.

Q. What are the requirements to use this service?
A. To access ACM Author-Izer, authors need to have a free ACM web account, must have an ACM Author Profile page in the Digital Library, and must take ownership of their Author Profile page.

Q. What is an ACM Author Profile Page?
A. The Author Profile Page initially collects all the professional information known about authors from the publications record as known by the ACM Digital Library. The Author Profile Page supplies a quick snapshot of an author's contribution to the field and some rudimentary measures of influence upon it. Over time, the contents of the Author Profile page may expand at the direction of the community. Please visit the ACM Author Profile documentation page for more background information on these pages.

Q. How do I find my Author Profile page and take ownership?
A. You will need to take the following steps:
- Create a free ACM Web Account
- Sign-In to the ACM Digital Library
- Find your Author Profile Page by searching the ACM Digital Library for your name
- Find the result you authored (where your author name is a clickable link)
- Click on your name to go to the Author Profile Page
- Click the "Add Personal Information" link on the Author Profile Page
- Wait for ACM review and approval; generally less than 24 hours

Q. Why does my photo not appear?
A. Make sure that the image you submit is in .jpg or .gif format and that the file name does not contain special characters

Q. What if I cannot find the Add Personal Information function on my author page?
A. The ACM account linked to your profile page is different than the one you are logged into. Please logout and login to the account associated with your Author Profile Page.

Q. What happens if an author changes the location of his bibliography or moves to a new institution?
A. Should authors change institutions or sites, they can utilize ACM Author-Izer to disable old links and re-authorize new links for free downloads from a new location.

Q. What happens if an author provides a URL that redirects to the author’s personal bibliography page?
A. The service will not provide a free download from the ACM Digital Library. Instead the person who uses that link will simply go to the Citation Page for that article in the ACM Digital Library where the article may be accessed under the usual subscription rules.

However, if the author provides the target page URL, any link that redirects to that target page will enable a free download from the Service.

Q. What happens if the author’s bibliography lives on a page with several aliases?
A. Only one alias will work, whichever one is registered as the page containing the author’s bibliography. ACM has no technical solution to this problem at this time.

Q. Why should authors use ACM Author-Izer?
A. ACM Author-Izer lets visitors to authors’ personal home pages download articles for no charge from the ACM Digital Library. It allows authors to dynamically display real-time download and citation statistics for each “authorized” article on their personal site.

Q. Does ACM Author-Izer provide benefits for authors?
A. Downloads of definitive articles via Author-Izer links on the authors’ personal web page are captured in official ACM statistics to more accurately reflect usage and impact measurements.

Authors who do not use ACM Author-Izer links will not have downloads from their local, personal bibliographies counted. They do, however, retain the existing right to post author-prepared preprint versions on their home pages or institutional repositories with DOI pointers to the definitive version permanently maintained in the ACM Digital Library.

Q. How does ACM Author-Izer benefit the computing community?
A. ACM Author-Izer expands the visibility and dissemination of the definitive version of ACM articles. It is based on ACM’s strong belief that the computing community should have the widest possible access to the definitive versions of scholarly literature. By linking authors’ personal bibliography with the ACM Digital Library, user confusion over article versioning should be reduced over time.

In making ACM Author-Izer a free service to both authors and visitors to their websites, ACM is emphasizing its continuing commitment to the interests of its authors and to the computing community in ways that are consistent with its existing subscription-based access model.

Q. How do authors access ACM Author-Izer?
A. See How to Use

Q. Why can’t I find my most recent publication in my ACM Author Profile Page?
A. There is a time delay between publication and the process which associates that publication with an Author Profile Page. Right now, that process usually takes 4-8 weeks.

Q. How does ACM Author-Izer expand ACM’s “Green Path” Access Policies?
A. ACM Author-Izer extends the rights and permissions that authors retain even after copyright transfer to ACM, which has been among the “greenest” publishers. ACM enables its author community to retain a wide range of rights related to copyright and reuse of materials. They include:
- Posting rights that ensure free access to their work outside the ACM Digital Library and print publications
- Rights to reuse any portion of their work in new works that they may create
- Copyright to artistic images in ACM’s graphics-oriented publications that authors may want to exploit in commercial contexts
- All patent rights, which remain with the original owner