In this paper, we investigate the leader election problem in diameter-two networks. Recently, Chatterjee et al. [DC 2020] studied the leader election in diameter-two networks. They presented a $O(\log n)$-round deterministic {implicit} leader election algorithm which incurs optimal $O(n\log n)$ messages, but a drawback of their algorithm is that it requires knowledge of $n$. An important question -- whether it is possible to remove the assumption on the knowledge of $n$ was left open in their paper. Another interesting open question raised in their paper is whether {\em explicit} leader election can be solved in $\tilde{O}(n)$ messages deterministically. In this paper, we give an affirmative answer to them. Further, we solve the {\em broadcast problem}, another fundamental problem in distributed computing, deterministically in diameter-two networks with $\tilde{O}(n)$ messages and $\tilde{O}(1)$ rounds without the knowledge of $n$. In fact, we address all the open questions raised by Chatterjee et al. for the deterministic leader election problem in diameter-two networks. To the best of our knowledge, this is the first $\tilde{O}(n)$ deterministic result for the explicit leader election in the diameter-two networks, that too without the knowledge of $n$.
Coordination in a distributed system is facilitated if there is a unique process, the leader, to manage the other processes. The leader creates edicts and sends them to other processes for execution or forwarding to other processes. The leader may fail, and when this occurs a leader election protocol selects a replacement. This paper describes Nerio, a class of such leader election protocols.
We study the time needed for deterministic leader election in the ${\cal LOCAL}$ model, where in every round a node can exchange any messages with its neighbors and perform any local computations. The topology of the network is unknown and nodes are unlabeled, but ports at each node have arbitrary fixed labelings which, together with the topology of the network, can create asymmetries to be exploited in leader election. We consider two versions of the leader election problem: strong LE in which exactly one leader has to be elected, if this is possible, while all nodes must terminate declaring …
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…
In this paper, the leader election problem in the population protocol model is considered. A leader election protocol with logarithmic stabilization time is given. Given a rough knowledge m of the population size n such that m >= \log_2 n and m=O(log n), the proposed protocol guarantees that exactly one leader is elected from n agents within O(log n) parallel time in expectation and the unique leader is kept forever thereafter. The number of states per agent of the protocol is O(log n).
There are many distributed systems which use a leader in their logic. When such systems need to be fault tolerant and the current leader suffers a technical problem, it is necesary to apply a special algorithm in order to choose a new leader. In this paper I present a new fault tolerant algorithm which elects a new leader based on a random roulette wheel selection.
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 …
This paper gives tight logarithmic lower bounds on the solo step complexity of leader election in an asynchronous shared-memory model with single-writer multi-reader (SWMR) registers, for randomized obstruction-free algorithms. The approach extends to lower bounds for randomized obstruction-free algorithms using multi-writer registers under bounded write concurrency, showing a trade-off between the solo step complexity of a leader election algorithm, and the worst-case contention incurred by a processor in an execution.
In this paper we present a framework for leader election in multi-hop radio networks which yield randomized leader election algorithms taking $O(\text{broadcasting time})$ in expectation, and another which yields algorithms taking fixed $O(\sqrt{\log n})$-times broadcasting time. Both succeed with high probability. We show how to implement these frameworks in radio networks without collision detection, and in networks with collision detection (in fact in the strictly weaker beep model). In doing so, we obtain the first optimal expected-time leader election algorithms in both settings, and also…
We propose a self-stabilizing leader election protocol on directed rings in the model of population protocols. Given an upper bound $N$ on the population size $n$, the proposed protocol elects a unique leader within $O(nN)$ expected steps starting from any configuration and uses $O(N)$ states. This convergence time is optimal if a given upper bound $N$ is asymptotically tight, i.e., $N=O(n)$.
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…
In this paper, we look at the problem of randomized leader election in synchronous distributed networks with a special focus on the message complexity. We provide an algorithm that solves the implicit version of leader election (where non-leader nodes need not be aware of the identity of the leader) in any general network with $O(\sqrt{n} \log^{7/2} n \cdot t_{mix})$ messages and in $O(t_{mix}\log^2 n)$ time, where $n$ is the number of nodes and $t_{mix}$ refers to the mixing time of a random walk in the network graph $G$. For several classes of well-connected networks (that have a large condu…
This paper focuses on studying the message complexity of implicit leader election in synchronous distributed networks of diameter two. Kutten et al.\ [JACM 2015] showed a fundamental lower bound of $Ω(m)$ ($m$ is the number of edges in the network) on the message complexity of (implicit) leader election that applied also to Monte Carlo randomized algorithms with constant success probability; this lower bound applies for graphs that have diameter at least three. On the other hand, for complete graphs (i.e., graphs with diameter one), Kutten et al.\ [TCS 2015] established a tight bound of $\tild…
This paper shows that every leader election protocol requires logarithmic stabilization time both in expectation and with high probability in the population protocol model. This lower bound holds even if each agent has knowledge of the exact size of a population and is allowed to use an arbitrarily large number of agent states. This lower bound concludes that the protocol given in [Sudo et al., SSS 2019] is time-optimal in expectation.
The model of population protocols refers to a large collection of simple indistinguishable entities, frequently called {\em agents}. The agents communicate and perform computation through pairwise interactions. We study fast and space efficient leader election in population of cardinality $n$ governed by a random scheduler, where during each time step the scheduler uniformly at random selects for interaction exactly one pair of agents. We propose the first $o(\log^2 n)$-time leader election protocol. Our solution operates in expected parallel time $O(\log n\log\log n)$ which is equivalent to $…
We consider the leader election problem in population protocol models. In pragmatic settings of population protocols, self-stabilization is a highly desired feature owing to its fault resilience and the benefit of initialization freedom. However, the design of self-stabilizing leader election is possible only under a strong assumption (i.e. the knowledge of the \emph{exact} size of a network) and rich computational resources (i.e. the number of states). Loose-stabilization, introduced by Sudo et al [Theoretical Computer Science, 2012], is a promising relaxed concept of self-stabilization to ad…
Leader-based consensus protocols must undergo a view-change phase to elect a new leader when the current leader fails. The new leader is often decided upon a candidate server that collects votes from a quorum of servers. However, voting-based election mechanisms intrinsically cause competition in leadership candidacy when each candidate collects only partial votes. This split-vote scenario can result in no leadership winner and prolong the undesired view-change period. In this paper, we investigate a case study of Raft's leader election mechanism and propose a new leader election protocol, cal…
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…
The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this paper the emphasis is on the space complexity in fast leader election via population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions within the population of n agents. The main result of this paper is a new fast and space optimal leader election protocol. The new protocol utilises O(log^2 n) parallel time (which …
We present fast deterministic distributed protocols in synchronous networks for leader election and spanning tree construction. The protocols are designed under the assumption that nodes in a network have identifiers but the size of an identifier is unlimited. So time bounds of protocols depend on the sizes of identifiers. We present fast protocols running in time $O(D\log L+L)$, where $L$ is the size of the minimal identifier and $D$ is the diameter of a network.
Population protocols are networks of finite-state agents, interacting randomly, and updating their states using simple rules. Despite their extreme simplicity, these systems have been shown to cooperatively perform complex computational tasks, such as simulating register machines to compute standard arithmetic functions. The election of a unique leader agent is a key requirement in such computational constructions. Yet, the fastest currently known population protocol for electing a leader only has linear stabilization time, and, it has recently been shown that no population protocol using a co…
Leader election is, together with consensus, one of the most central problems in distributed computing. This paper presents a distributed algorithm, called \STT, for electing deterministically a leader in an arbitrary network, assuming processors have unique identifiers of size $O(\log n)$, where $n$ is the number of processors. It elects a leader in $O(D +\log n)$ rounds, where $D$ is the diameter of the network, with messages of size $O(1)$. Thus it has a bit round complexity of $O(D +\log n)$. This substantially improves upon the best known algorithm whose bit round complexity is $O(D\log n…
This paper concerns {\em randomized} leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete $n$-node networks that runs in O(1) rounds and (with high probability) uses only $O(\sqrt{n}\log^{3/2} n)$ messages to elect a unique leader (with high probability). When considering the "explicit" variant of leader election where eventually every node knows the identity of the leader, our algorithm yields the asymptotically optimal bounds of O(1) rounds and O(n) messages. This algorithm is then extended to one solving leader election on an…
We study two fundamental communication primitives: broadcasting and leader election in the classical model of multi-hop radio networks with unknown topology and without collision detection mechanisms. It has been known for almost 20 years that in undirected networks with n nodes and diameter D, randomized broadcasting requires Omega(D log n/D + log^2 n) rounds in expectation, assuming that uninformed nodes are not allowed to communicate (until they are informed). Only very recently, Haeupler and Wajc (PODC'2016) showed that this bound can be slightly improved for the model with spontaneous tra…
We study a game theoretic model where a coalition of processors might collude to bias the outcome of the protocol, where we assume that the processors always prefer any legitimate outcome over a non-legitimate one. We show that the problems of Fair Leader Election and Fair Coin Toss are equivalent, and focus on Fair Leader Election. Our main focus is on a directed asynchronous ring of $n$ processors, where we investigate the protocol proposed by Abraham et al. \cite{abraham2013distributed} and studied in Afek et al. \cite{afek2014distributed}. We show that in general the protocol is resilient …
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^…
We consider the model of population protocols, which can be viewed as a sequence of random pairwise interactions of $n$ agents (nodes). We show population protocols for two problems: the leader election and the exact majority voting. The leader election starts with all agents in the same initial state and the goal is to converge to the (global) state when exactly one agent is in a distinct state $L$. The exact majority voting starts with each agent in one of the two distinct states $A$ or $B$ and the goal is to make all nodes know which of these two states was the initial majority state, even …
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…
This paper presents a randomized self-stabilizing algorithm that elects a leader $r$ in a general $n$-node undirected graph and constructs a spanning tree $T$ rooted at $r$. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on $n$ and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the $KT_{1}$ model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of $\tilde{O} (n)$ messages, each of constant size, till stabilization, whil…
In asynchronous distributed systems it is very hard to assess if one of the processes taking part in a computation is operating correctly or has failed. To overcome this problem, distributed algorithms are created using unreliable failure detectors that capture in an abstract way timing assumptions necessary to assess the operating status of a process. One particular type of failure detector is a leader election, that indicates a single process that has not failed. The unreliability of these failure detectors means that they can make mistakes, however if they are to be used in practice there m…
This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the protocol is required to be \emph{silent} (i.e., when communication content remains fixed from some point in time during any execution), there exists a lower bound of Omega(\log n) bits of memory per node participating to the leader election (where n denotes the number of nodes in the system). This lower bound holds even in rings. We present a new deterministic (non-silent) self-stabilizing protocol for n-node rings that uses only O(\log\log n) memory bits per node, and stabilizes in…
Electing a leader is a classical problem in distributed computing system. Synchronization between processes often requires one process acting as a coordinator. If an elected leader node fails, the other nodes of the system need to elect another leader without much wasting of time. The bully algorithm is a classical approach for electing a leader in a synchronous distributed computing system, which is used to determine the process with highest priority number as the coordinator. In this paper, we have discussed the limitations of Bully algorithm and proposed a simple and efficient method for th…
Mobile Ad Hoc networks (MANET), distinct from traditional distributed systems, are dynamic and self-organizing networks. MANET requires a leader to coordinate and organize tasks. The challenge is to have the right election algorithm that chooses the right leader based on various factors in MANET. In this paper, we analyze four leader election algorithms used in mobile Ad Hoc Networks. Factors considered in our analysis are time complexity, message complexity, assumptions considered, fault tolerance and timing model. Our proposed enhancements include recovered nodes inquiring about the current …
We present a self-stabilizing leader election algorithm for arbitrary networks, with space-complexity $O(\max\{\log Δ, \log \log n\})$ bits per node in $n$-node networks with maximum degree~$Δ$. This space complexity is sub-logarithmic in $n$ as long as $Δ= n^{o(1)}$. The best space-complexity known so far for arbitrary networks was $O(\log n)$ bits per node, and algorithms with sub-logarithmic space-complexities were known for the ring only. To our knowledge, our algorithm is the first algorithm for self-stabilizing leader election to break the $Ω(\log n)$ bound for silent algorithms in arbit…
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, assumin…
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…
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 …
The different functions of a leader node in Ad hoc networks, particularly in Wireless Sensor Networks (WSNs) and Internet of Things (IoT) include generation of keys for encryption/decryption, finding a node with minimum energy or node located in an extreme side of the network. One essential application of IoT is to monitor any dangerous, sensitive or non-accessible site. Such type of application requires the election of a leader located on the extreme left of the network. Indeed, one can then use any leader election (LE) algorithm to find this node, and then start the process of finding its bo…
This paper concerns designing distributed algorithms that are {\em singularly optimal}, i.e., algorithms that are {\em simultaneously} time and message {\em optimal}, for the fundamental leader election problem in {\em asynchronous} networks. Kutten et al. (JACM 2015) presented a singularly near optimal randomized leader election algorithm for general {\em synchronous} networks that ran in $O(D)$ time and used $O(m \log n)$ messages (where $D$, $m$, and $n$ are the network's diameter, number of edges and number of nodes, respectively) with high probability.\footnote{Throughout, "with high prob…
Electing leader is a vital issue not only in distributed computing but also in communication network [1, 2, 3, 4, 5], centralized mutual exclusion algorithm [6, 7], centralized control IPC, etc. A leader is required to make synchronization between different processes. And different election algorithms are used to elect a coordinator among the available processes in the system such a way that there will be only one coordinator at any time. Bully election algorithm is one of the classical and well-known approaches in coordinator election process. This paper will present a modified version of bul…
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 …
Addressing a fundamental problem in programmable matter, we present the first deterministic algorithm to elect a unique leader in a system of connected amoebots assuming only that amoebots are initially contracted. Previous algorithms either used randomization, made various assumptions (shapes with no holes, or known shared chirality), or elected several co-leaders in some cases. Some of the building blocks we introduce in constructing the algorithm are of interest by themselves, especially the procedure we present for reaching common chirality among the amoebots. Given the leader election and…
This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in networks. Our main result is a randomized distributed leader election algorithm for asynchronous complete networks that is essentially (up to a polylogarithmic factor) singularly optimal. Our algorithm uses $O(n)$ messages with high probability and runs in $O(\log^2 n)$ time (with high probability) to elect a unique leader. The $O(n)$ message complexity should be contrasted with the $Ω(n \log n)$ lowe…
