Dynamic Asynchronous Iterations

by   Matthew L. Daggitt, et al.

Many problems can be solved by iteration by multiple participants (processors, servers, routers etc.). Previous mathematical models for such asynchronous iterations assume a single function being iterated by a fixed set of participants. We will call such iterations static since the system's configuration does not change. However in several real-world examples, such as inter-domain routing, both the function being iterated and the set of participants change frequently while the system continues to function. In this paper we extend Uresin Dubois's work on static iterations to develop a model for this class of "dynamic" or "always on" asynchronous iterations. We explore what it means for such an iteration to be implemented correctly, and then prove two different conditions on the set of iterated functions that guarantee the full asynchronous iteration satisfies this new definition of correctness. These results have been formalised in Agda and the resulting library is publicly available.



There are no comments yet.


page 1

page 2

page 3

page 4


Asynchronous Richardson iterations

We consider asynchronous versions of the first and second order Richards...

Asynchronous Parareal Algorithm Applied to European Option Pricing

Asynchronous iterations arise naturally in parallel computing if one wan...

More Iterations per Second, Same Quality -- Why Asynchronous Algorithms may Drastically Outperform Traditional Ones

In this paper, we consider the convergence of a very general asynchronou...

An Asynchronous Distributed Framework for Large-scale Learning Based on Parameter Exchanges

In many distributed learning problems, the heterogeneous loading of comp...

Delayed Asynchronous Iterative Graph Algorithms

Iterative graph algorithms often compute intermediate values and update ...

Convergence Detection of Asynchronous Iterations based on Modified Recursive Doubling

This paper addresses the distributed convergence detection problem in as...

On the serial connection of the regular asynchronous systems

The asynchronous systems f are multi-valued functions, representing the ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.