https://arxiv.org/abs/2311.06281

Skip to main content
Cornell University
We gratefully acknowledge support from the Simons Foundation, member
institutions, and all contributors. Donate
 
arxiv logo > cs > arXiv:2311.06281
[                    ]

Help | Advanced Search

[All fields        ]
Search
arXiv logo
Cornell University Logo
[                    ] GO
quick links

  * Login
  * Help Pages
  * About

Computer Science > Data Structures and Algorithms

arXiv:2311.06281 (cs)
[Submitted on 27 Oct 2023 (v1), last revised 15 Nov 2023 (this
version, v2)]

Title:Efficient Parallelization of an Ubiquitous Sequential
Computation

Authors:Franz A. Heinsen
Download a PDF of the paper titled Efficient Parallelization of an
Ubiquitous Sequential Computation, by Franz A. Heinsen
Download PDF

    Abstract:We find a succinct expression for computing the sequence
    $x_t = a_t x_{t-1} + b_t$ in parallel with two prefix sums, given
    $t = (1, 2, \dots, n)$, $a_t \in \mathbb{R}^n$, $b_t \in \mathbb
    {R}^n$, and initial value $x_0 \in \mathbb{R}$. On $n$ parallel
    processors, the computation of $n$ elements incurs $\mathcal{O}(\
    log n)$ time and $\mathcal{O}(n)$ space. Sequences of this form
    are ubiquitous in science and engineering, making efficient
    parallelization useful for a vast number of applications. We
    implement our expression in software, test it on parallel
    hardware, and verify that it executes faster than sequential
    computation by a factor of $\frac{n}{\log n}$.

Comments: Source code for replicating our results is available online
          at this https URL
Subjects: Data Structures and Algorithms (cs.DS); Machine Learning
          (cs.LG)
Cite as:  arXiv:2311.06281 [cs.DS]
          (or arXiv:2311.06281v2 [cs.DS] for this version)
          https://doi.org/10.48550/arXiv.2311.06281
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Franz Heinsen [view email]
[v1] Fri, 27 Oct 2023 21:58:55 UTC (112 KB)
[v2] Wed, 15 Nov 2023 14:53:19 UTC (112 KB)
Full-text links:

Access Paper:

    Download a PDF of the paper titled Efficient Parallelization of
    an Ubiquitous Sequential Computation, by Franz A. Heinsen
  * Download PDF
  * PostScript
  * Other Formats

[by-4]
Current browse context:
cs.DS
< prev   |   next >
new | recent | 2311
Change to browse by:
cs
cs.LG

References & Citations

  * NASA ADS
  * Google Scholar
  * Semantic Scholar

a export BibTeX citation Loading...

BibTeX formatted citation

x
[loading...          ]
Data provided by:

Bookmark

BibSonomy logo Reddit logo
(*) Bibliographic Tools

Bibliographic and Citation Tools

[ ] Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
[ ] Litmaps Toggle
Litmaps (What is Litmaps?)
[ ] scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
( ) Code, Data, Media

Code, Data and Media Associated with this Article

[ ] Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
[ ] DagsHub Toggle
DagsHub (What is DagsHub?)
[ ] Links to Code Toggle
Papers with Code (What is Papers with Code?)
[ ] ScienceCast Toggle
ScienceCast (What is ScienceCast?)
( ) Demos

Demos

[ ] Replicate Toggle
Replicate (What is Replicate?)
[ ] Spaces Toggle
Hugging Face Spaces (What is Spaces?)
( ) Related Papers

Recommenders and Search Tools

[ ] Link to Influence Flower
Influence Flower (What are Influence Flowers?)
[ ] Connected Papers Toggle
Connected Papers (What is Connected Papers?)
[ ] Core recommender toggle
CORE Recommender (What is CORE?)

  * Author
  * Venue
  * Institution
  * Topic

( ) About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and
share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have
embraced and accepted our values of openness, community, excellence,
and user data privacy. arXiv is committed to these values and only
works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community?
Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is
MathJax?)

  * About
  * Help

  * Click here to contact arXiv Contact
  * Click here to subscribe Subscribe

  * Copyright
  * Privacy Policy

  * Web Accessibility Assistance
  * arXiv Operational Status
    Get status notifications via email or slack