We address the Leader Election (LE) problem in networks of anonymous sensors sharing no kind of common coordinate system. Leader Election is a fundamental symmetry breaking problem in distributed computing. Its goal is to assign value 1 (leader) to one of the entities and value 0 (non-leader) to all others. In this paper, assuming n > 1 disoriented anonymous sensors, we provide a complete charac- terization on the sensors positions to deterministically elect a leader, provided that all the sensors' positions are known by every sensor. More precisely, our contribution is twofold: First, assuming n anonymous sensors agreeing on a common handedness (chirality) of their own coordinate system, we provide a complete characterization on the sensors positions to deterministically elect a leader. Second, we also provide such a complete chararacterization for sensors devoided of a common handedness. Both characterizations rely on a particular object from combinatorics on words, namely the Lyndon Words.
This article addresses election in fully anonymous systems made up of $n$ asynchronous processes that communicate through atomic read-write registers or atomic read-modify-write registers. Given an integer $d\in\{1,\dots, n-1\}$, two elections problems are considered: $d$-election (at least one and at most $d$ processes are elected) and exact $d$-election (exactly $d$ processes are elected). Full anonymity means that both the processes and the shared registers are anonymous. Memory anonymity means that the processes may disagree on the names of the shared registers. That is, the same register …
We study the problem of randomized Leader Election in synchronous distributed networks with indistinguishable nodes. We consider algorithms that work on networks of arbitrary topology in two settings, depending on whether the size of the network, i.e., the number of nodes, is known or not. In the former setting, we present a new Leader Election protocol that improves over previous work by lowering message complexity and making it close to a lower bound by a factor of $\tilde{O}(\sqrt{t_{mix}\sqrtΦ})$, where $Φ$ is the conductance and $t_{mix}$ is the mixing time of the network graph. We then s…
We study the problem of leader election among mobile agents operating in an arbitrary network modeled as an undirected graph. Nodes of the network are unlabeled and all agents are identical. Hence the only way to elect a leader among agents is by exploiting asymmetries in their initial positions in the graph. Agents do not know the graph or their positions in it, hence they must gain this knowledge by navigating in the graph and share it with other agents to accomplish leader election. This can be done using meetings of agents, which is difficult because of their asynchronous nature: an advers…
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 'non-leader', or in a strong way, where all nodes must also learn which node is the leader. If the nodes of the network have distinct identifiers, then such an agreement means that all nodes have to output the identifier of the elected leader. For anonymous networks, the strong version of leader election requires that all nodes must be able to find a path to …
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, coded as a sequence of port numbers, such that all these paths end at a common node, the leader. In this paper, we study deterministic leader election in anonymous trees. Our aim is to establish tradeoffs between the allocated time $τ$ and the amount of information that has to be given $\textit{a priori}$ to the nodes to enable leader election in time $τ$ in …
We consider leader election in anonymous radio networks modeled as simple undirected connected graphs. Nodes communicate in synchronous rounds. Nodes are anonymous and execute the same deterministic algorithm, so symmetry can be broken only in one way: by different wake-up times of the nodes. In which situations is it possible to break symmetry and elect a leader using time as symmetry breaker? To answer this question, we consider configurations. A configuration is the underlying graph with nodes tagged by non-negative integers with the following meaning. A node can either wake up spontaneousl…
Remote voting has become more critical in recent years, especially after the Covid-19 outbreak. Blockchain technology and its benefits like decentralization, security, and transparency have encouraged remote voting systems to use blockchains. Analysis of existing solutions reveals that anonymity, robustness, and scalability are common problems in blockchain-based election systems. In this work, we propose ElectAnon, a blockchain-based, ranked-choice election protocol focusing on anonymity, robustness, and scalability. ElectAnon achieves anonymity by enabling voters to cast their votes via zero…
University of Strasbourg（斯特拉斯堡大学）；University Clermont Auvergne（克莱蒙奥弗涅大学）
We deal with a set of autonomous robots moving on an infinite grid. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global compass. Finally, they may use lights of different colors, but except from that, robots have neither persistent memories, nor communication mean. We consider the infinite grid exploration (IGE) problem. For this problem we give two impossibility results and three algorithms, including one which is optimal in terms of number of robots. In more detail, we firs…
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 that all nodes have to output the label of the elected leader. If the nodes are anonymous, the task of leader election is formulated as follows: every node of the network must output a simple path starting at it, which is coded as a sequence of port numbers, such that all these paths end at a common node, the leader. In this paper, we study deterministic lea…
We study the problems of leader election and population size counting for population protocols: networks of finite-state anonymous agents that interact randomly under a uniform random scheduler. We show a protocol for leader election that terminates in $O(\log_m(n) \cdot \log_2 n)$ parallel time, where $m$ is a parameter, using $O(\max\{m,\log n\})$ states. By adjusting the parameter $m$ between a constant and $n$, we obtain a single leader election protocol whose time and space can be smoothly traded off between $O(\log^2 n)$ to $O(\log n)$ time and $O(\log n)$ to $O(n)$ states. Finally, we g…
Leader election and arbitrary pattern formation are funda- mental tasks for a set of autonomous mobile robots. The former consists in distinguishing a unique robot, called the leader. The latter aims in arranging the robots in the plane to form any given pattern. The solv- ability of both these tasks turns out to be necessary in order to achieve more complex tasks. In this paper, we study the relationship between these two tasks in a model, called CORDA, wherein the robots are weak in several aspects. In particular, they are fully asynchronous and they have no direct means of communication. Th…
Two anonymous mobile agents navigate synchronously in an anonymous graph and have to meet at a node, using a deterministic algorithm. This is a symmetry breaking task called rendezvous, equivalent to the fundamental task of leader election between the agents. When is this feasible in a completely anonymous environment? It is known that agents can always meet if their initial positions are nonsymmetric, and that if they are symmetric and agents start simultaneously then rendezvous is impossible. What happens for symmetric initial positions with non-simultaneous start? Can symmetry between the a…
This paper proposes a distributed algorithm which deterministically gathers n (n > 4) asynchronous, fat robots. The robots are assumed to be transparent and they have full visibility. The robots are initially considered to be stationary. A robot is visible in its motion. The robots do not store past actions. They are anonymous and can not be distinguished by their appearances and do not have common coordinate system or chirality. The robots do not communicate through message passing. In the proposed gathering algorithm one robot moves at a time towards its destination. The robot which moves, i…
We consider the standard population protocol model, where (a priori) indistinguishable and anonymous agents interact in pairs according to uniformly random scheduling. The self-stabilizing leader election problem requires the protocol to converge on a single leader agent from any possible initial configuration. We initiate the study of time complexity of population protocols solving this problem in its original setting: with probability 1, in a complete communication graph. The only previously known protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time $Θ(n^…
Population protocols are a relatively novel computational model in which very resource-limited anonymous agents interact in pairs with the goal of computing predicates. We consider the probabilistic version of this model, which naturally allows to consider the setup in which a small probability of an incorrect output is tolerated. The main focus of this thesis is the question of confident leader election, which is an extension of the regular leader election problem with an extra requirement for the eventual leader to detect its uniqueness. Having a confident leader allows the population protoc…
Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic algorithms. This paper aims at studying randomized synchronous distributed computing through the lens of algebraic topology. We do so by studying the wide class of (input-free) symmetry-breaking tasks, e.g., leader election, in synchronous fault-free anonymous systems. We show that it is possible to redefine solvability of a task "locally", i.e., for each simpl…
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 single node adopting the label 1 (leader), with all other nodes adopting the label 0 and learning a path to the leader. We consider both these problems in networks whose nodes are equipped with not necessarily distinct labels called colors, and ports at each node of degree $d$ are arbitrarily numbered $0,1,\dots, d-1$. Colored networks are generalizations both …
