2 research outputs found
Ordered and delayed adversaries and how to work against them on a shared channel
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 performance of algorithms. We focus on the Do-All
problem of performing t tasks on a shared channel consisting of p crash-prone
stations. The channel restricts communication: no message is delivered to the
alive stations if more than one station transmits at the same time. The
performance measure for the Do-All problem is work: the total number of
available processor steps during the whole execution. We address the question
of how the ordered adversaries controlling crashes of stations influence work
performance of Do-All algorithms. The first presented algorithm solves Do-All
with work O(t+p\sqrt{t}\log p) against the Linearly-Ordered adversary,
restricted by some pre-defined linear order of crashing stations. Another
algorithm runs against the Weakly-Adaptive adversary, restricted by some
pre-defined set of f crash-prone stations (it can be seen as restricted by the
order being an anti-chain of crashing stations). The work done by this
algorithm is O(t+p\sqrt{t}+p\min{p/(p-f),t}\log p). Both results are close to
the corresponding lower bounds from [CKL]. We generalize this result to the
class of adversaries restricted by a partial order with a maximum anti-chain of
size k and complement with the lower bound. We also consider a class of delayed
adaptive adversaries, who could see random choices with some delay. We give an
algorithm that runs against the 1-RD adversary (seeing random choices of
stations with one round delay), achieving close to optimal O(t+p\sqrt{t}\log^2
p) work complexity. This shows that restricting adversary by even 1 round delay
results in (almost) optimal work on a shared channel