12 research outputs found
Distributed Computing in the Asynchronous LOCAL model
The LOCAL model is among the main models for studying locality in the
framework of distributed network computing. This model is however subject to
pertinent criticisms, including the facts that all nodes wake up
simultaneously, perform in lock steps, and are failure-free. We show that
relaxing these hypotheses to some extent does not hurt local computing. In
particular, we show that, for any construction task associated to a locally
checkable labeling (LCL), if is solvable in rounds in the LOCAL model,
then remains solvable in rounds in the asynchronous LOCAL model.
This improves the result by Casta\~neda et al. [SSS 2016], which was restricted
to 3-coloring the rings. More generally, the main contribution of this paper is
to show that, perhaps surprisingly, asynchrony and failures in the computations
do not restrict the power of the LOCAL model, as long as the communications
remain synchronous and failure-free
List Defective Colorings: Distributed Algorithms and Applications
The distributed coloring problem is at the core of the area of distributed
graph algorithms and it is a problem that has seen tremendous progress over the
last few years. Much of the remarkable recent progress on deterministic
distributed coloring algorithms is based on two main tools: a) defective
colorings in which every node of a given color can have a limited number of
neighbors of the same color and b) list coloring, a natural generalization of
the standard coloring problem that naturally appears when colorings are
computed in different stages and one has to extend a previously computed
partial coloring to a full coloring.
In this paper, we introduce \emph{list defective colorings}, which can be
seen as a generalization of these two coloring variants. Essentially, in a list
defective coloring instance, each node is given a list of colors
together with a list of defects
such that if is colored with color , it is allowed to have at
most neighbors with color .
We highlight the important role of list defective colorings by showing that
faster list defective coloring algorithms would directly lead to faster
deterministic -coloring algorithms in the LOCAL model. Further, we
extend a recent distributed list coloring algorithm by Maus and Tonoyan [DISC
'20]. Slightly simplified, we show that if for each node it holds that
then
this list defective coloring instance can be solved in a
communication-efficient way in only communication rounds. This
leads to the first deterministic -coloring algorithm in the
standard CONGEST model with a time complexity of , matching the best time complexity in the LOCAL model up to a
factor