Related papers: Proving there is a leader without naming it
An impressive recent line of work has charted the complexity landscape of distributed graph algorithms. For many settings, it has been determined which time complexities exist, and which do not (in the sense that no local problem could have…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate is assigned to…
We study verification (decision) problems for graph properties in distributed networks under the locally checkable labeling framework, where nodes use labels (proofs) and local neighborhoods to decide acceptance or rejection. Our focus is…
On the one hand, the correctness of routing protocols in networks is an issue of utmost importance for guaranteeing the delivery of messages from any source to any target. On the other hand, a large collection of routing schemes have been…
A Locally Checkable Labeling (LCL) is a specification describing a set of labels that are valid with respect to a set of conditions that characterize a local part of a solution to a global problem. Conditions can only refer to nodes and…
An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…
Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
In this paper, we study the problem of certifying whether a graph is bipartite (i.e. $2$-colorable) with a locally checkable proof (LCP) that is able to hide a $2$-coloring from the verifier. More precisely, we say an LCP for $2$-coloring…
Proof-labeling schemes are known mechanisms providing nodes of networks with certificates that can be verified locally by distributed algorithms. Given a boolean predicate on network states, such schemes enable to check whether the…
In this paper, we investigate how local rules enforced at every node can influence the topology of a network. More precisely, we establish several results on the diameter of trees as a function of the number of nodes, as listed below. These…
Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…
In the distributed subgraph-freeness problem, we are given a graph $H$, and asked to determine whether the network graph contains $H$ as a subgraph or not. Subgraph-freeness is an extremely local problem: if the network had no bandwidth…
We study the power of \textit{local information algorithms} for optimization problems on social networks. We focus on sequential algorithms for which the network topology is initially unknown and is revealed only within a local neighborhood…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions…
In topology recognition, each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph, with all ports correctly marked. This task is usually unfeasible without any a priori information. Such…
Localization is a fundamental task for sensor networks. Traditional network construction approaches allow to obtain localized networks requiring the nodes to be at least tri-connected (in 2D), i.e., the communication graph needs to be…
In this work, we provide an upper bound for global certification of graph homomorphism, a generalization of graph coloring. In certification, the nodes of a network should decide if the network satisfies a given property, thanks to small…