4 papers
On the solution of Waring Problem with a multiplicative error term: dimension free estimates
Jarosław Mirek, Wojciech Słomian, Błażej Wróbel
We give a relation between the radius and the dimension in which the asymptotic formula in the Waring problem holds in a multiplicative and dimension-free fashion.
On the complexity of fault-tolerant consensus
Dariusz R. Kowalski, Jaroslaw Mirek
The paper studies the problem of reaching agreement in a distributed message-passing system prone to crash failures. Crashes are generated by \constrained\ adversaries - a \wadapt\…
Fault-tolerant parallel scheduling of arbitrary length jobs on a shared channel
Marek Klonowski, Dariusz R. Kowalski, Jarosław Mirek +1
We study the problem of scheduling jobs on fault-prone machines communicating via a shared channel, also known as multiple-access channel. We have arbitrary length jobs to be s…
Ordered and Delayed Adversaries and How to Work against Them on a Shared Channel
Marek Klonowski, Dariusz R. Kowalski, Jaroslaw Mirek
In this work we define a class of ordered adversaries causing distractions according to some partial order fixed by the adversary before the execution, and study how they affect pe…