arXiv subjects

Mikaël Rabie

Publications and source records attributed to Mikaël Rabie.

21 records · Page 2Linked to original sources

arXiv2019

The distributed complexity of locally checkable problems on paths is decidable

Consider a computer network that consists of a path with $n$ nodes. The nodes are labeled with inputs from a constant-sized set, and the task is to find output labels from a constant-sized set subject to some local constraints---more formally, we have an LCL (locally checkable labeling) problem. How many communication rounds are needed (in the standard LOCAL model of computing) to solve this problem? It is well known that the answer is always either $O(1)$ rounds, or $Θ(\log^* n)$ rounds, or $Θ(n)$ rounds. In this work we show that this question is decidable (albeit PSPACE-hard): we present an algorithm that, given any LCL problem defined on a path, outputs the distributed computational complexity of this problem and the corresponding asymptotically optimal algorithm.

cs.DC↗

arXiv2019

Distributed Recoloring

Given two colorings of a graph, we consider the following problem: can we recolor the graph from one coloring to the other through a series of elementary changes, such that the graph is properly colored after each step? We introduce the notion of distributed recoloring: The input graph represents a network of computers that needs to be recolored. Initially, each node is aware of its own input color and target color. The nodes can exchange messages with each other, and eventually each node has to stop and output its own recoloring schedule, indicating when and how the node changes its color. The recoloring schedules have to be globally consistent so that the graph remains properly colored at each point, and we require that adjacent nodes do not change their colors simultaneously. We are interested in the following questions: How many communication rounds are needed (in the LOCAL model of distributed computing) to find a recoloring schedule? What is the length of the recoloring schedule? And how does the picture change if we can use extra colors to make recoloring easier? The main contributions of this work are related to distributed recoloring with one extra color in the following graph classes: trees, $3$-regular graphs, and toroidal grids.

cs.DC↗

arXiv2016

Homonym Population Protocols

The population protocol model was introduced by Angluin \emph{et al.} as a model of passively mobile anonymous finite-state agents. This model computes a predicate on the multiset of their inputs via interactions by pairs. The original population protocol model has been proved to compute only semi-linear predicates and has been recently extended in various ways. In the community protocol model by Guerraoui and Ruppert, agents have unique identifiers but may only store a finite number of the identifiers they already heard about. The community protocol model provides the power of a Turing machine with a $O(n\log n)$ space. We consider variations on the two above models and we obtain a whole landscape that covers and extends already known results. Namely, by considering the case of homonyms, that is to say the case when several agents may share the same identifier, we provide a hierarchy that goes from the case of no identifier (population protocol model) to the case of unique identifiers (community protocol model). We obtain in particular that any Turing Machine on space $O(\log^{O(1)} n)$ can be simulated with at least $O(\log^{O(1)} n)$ identifiers, a result filling a gap left open in all previous studies. Our results also extend and revisit in particular the hierarchy provided by Chatzigiannakis \emph{et al.} on population protocols carrying Turing Machines on limited space, solving the problem of the gap left by this work between per-agent space $o(\log \log n)$ (proved to be equivalent to population protocols) and $O(\log n)$ (proved to be equivalent to Turing machines).

cs.DC↗