Related papers: Election vs. Selection: Two Ways of Finding the La…
Leader election is a basic symmetry breaking problem in distributed computing. All nodes of a network have to agree on a single node, called the leader. If the nodes of the network have distinct labels, then agreeing on a single node means…
Topology recognition and leader election are fundamental tasks in distributed computing in networks. The first of them requires each node to find a labeled isomorphic copy of the network, while the result of the second one consists in a…
We consider the task of graph exploration. An $n$-node graph has unlabeled nodes, and all ports at any node of degree $d$ are arbitrarily numbered $0,\dots, d-1$. A mobile agent has to visit all nodes and stop. The exploration time is the…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
Leader election is one of the basic problems in distributed computing. For anonymous networks, the task of leader election is formulated as follows: every node v of the network must output a simple path, which is coded as a sequence of port…
In this work we study local computation with advice: the goal is to solve a graph problem $\Pi$ with a distributed algorithm in $T(\Delta)$ communication rounds, for some function $T$ that only depends on the maximum degree $\Delta$ of the…
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…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
The leader election task calls for all nodes of a network to agree on a single node. If the nodes of the network are anonymous, the task of leader election is formulated as follows: every node $v$ of the network must output a simple path,…
The number of nodes of a network, called its size, and the largest distance between nodes of a network, called its diameter, are among the most important network parameters. Knowing the size and/or diameter is a prerequisite of many…
We consider two fundamental communication tasks in arbitrary radio networks: broadcasting (information from one source has to reach all nodes) and gossiping (every node has a message and all messages have to reach all nodes). Nodes are…
When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…
We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
Leader election is one of the fundamental problems in distributed computing: a single node, called the leader, must be specified. This task can be formulated either in a weak way, where one node outputs 'leader' and all other nodes output…
We consider the fundamental problems of size discovery and topology recognition in radio networks modeled by simple undirected connected graphs. Size discovery calls for all nodes to output the number of nodes in the graph, called its size,…
While there exists a wide variety of graph neural networks (GNN) for node classification, only a minority of them adopt mechanisms that effectively target noise propagation during the message-passing procedure. Additionally, a very…
The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts - including ranking websites - and can be interpreted as the average portion of time spent at…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
The election is a classical problem in distributed algorithmic. It aims to design and to analyze a distributed algorithm choosing a node in a graph, here, in a tree. In this paper, a class of randomized algorithms for the election is…