leader election

Unreliable failure detectors provide information about process failures. A particular failure detector called Omega has been shown to be the weakest for solving consensus with a majority of correct processes. This work addresses the implementation of Omega in the crash-recovery failure model. Firstly, the definition of Omega is adapted to that model, assuming that processes do not use stable storage. After that, an algorithm implementing Omega under some weak assumptions on communication reliability and synchrony is proposed.

This work addresses the leader election problem in partially synchronous distributed systems where processes can crash and recover. More precisely, it focuses on implementing the Omega failure detector class, which provides a leader election functionality, in the crash-recovery failure model. The concepts of communication efficiency and near-efficiency for an algorithm implementing Omega are defined. Depending on the use or not of stable storage, the property satisfied by unstable processes, i.e., those that crash and recover infinitely often, varies. Two algorithms implementing Omega are presented. In the first algorithm, which is communication-efficient and uses stable storage, eventually and permanently unstable processes agree on the leader with correct processes. In the second algorithm, which is nearcommunication-efficient and does not use stable storage, processes start their execution with no leader in order to avoid the disagreement among unstable processes, that will agree on the leader with correct processes after receiving a first message from the leader.

This paper presents a new algorithm implementing the Omega failure detector in the crash-recovery model. Contrary to previously proposed algorithms, this algorithm does not rely on the use of stable storage and is communication-efficient, i.e., eventually only one process (the elected leader) keeps sending messages. The algorithm relies on a nondecreasing local clock associated with each process. Since stable storage is not used to keep the identity of the leader in order to read it upon recovery, unstable processes, i.e., those that crash and recover infinitely often, output a special ⊥ value upon recovery, and then agree with correct processes on the leader after receiving a first message from it.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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. In a nutshell, this approach consists of capturing all the possible states of a distributed system at a certain time as a simplicial complex P(t), called protocol complex, and viewing computation as a simplicial map from that complex to the so-called output complex, O, that captures all possible legal output states of the system. The topological properties (e.g., homotopy) of the protocol complex depends on the

Lattice agreement is a key decision problem in distributed systems. In this problem, processes start with input values from a lattice, and must learn (non-trivial) values that form a chain. Unlike consensus, which is impossible in the presence of even a single process failure, lattice agreement has been shown to be decidable in the presence of failures. In this paper, we consider lattice agreement problems in asynchronous, message passing systems. We present an algorithm for the lattice agreement problem that guarantees liveness as long as a majority of the processes are non-faulty. The algorithm has a time complexity of O(N ) message delays, where N is the number of processes. We then introduce the generalized lattice agreement problem, where each process receives a (potentially unbounded) sequence of values from an infinite lattice and must learn a sequence of increasing values such that the union of all learnt sequences is a chain and every proposed value is eventually learnt. We present a wait-free algorithm for solving generalized lattice agreement. The algorithm guarantees that every value received by a correct process is learnt in O(N ) message delays. We show that this algorithm can be used to implement a class of replicated state machines where (a) commands can be classified as reads and updates, and (b) all update commands commute. This algorithm can be used to realize serializable and linearizable replicated versions of commonly used data types.

Leader election is one of the core coordination problems of distributed systems, and has been addressed in many different ways suitable for different classes of systems. It is unclear, however, whether existing methods will be effective for resilient device coordination in open, complex, networked distributed systems like smart cities, tactical networks, personal networks and the Internet of Things (IoT). Aggregate computing provides a layered approach to developing such systems, in which resilience is provided by a layer comprising a set of adaptive algorithms whose compositions have been shown to cover a large class of coordination activities. In this paper, we show how a feedback interconnection of these basis set algorithms can perform distributed leader election resilient to device topology and position changes. We also characterize a key design parameter that defines some important performance attributes: Too large a value impairs resilience to loss of existing leaders, while too small a value leads to multiple leaders. We characterize the smallest value of this parameter for which the only stationary points have single leaders, and demonstrate resilience of this algorithm through simulations.

We i n v estigate the problem of self-stabilizing round-robin token management s c heme on an anonymous bidirectional ring of identical processors, where each processor is an asynchronous probabilistic coin-ipping nite state machine which sends and receives messages. We show that the solution to this problem is equivalent to symmetry breaking i.e., leader election. Requiring only constant-size messages and message-passing model has practical implications: our solution can be implemented in high-speed networks using a universal fast hardware switches i.e., nite state machines of size independent of the size of the network. Our automata-based message-passing model has inherent deadlock possibility i.e., when all processors are waiting for a message which w e assume is detected by an external timeout mechanism. Provided that there is no deadlock to begin with, we show h o w starting from an arbitrary con guration, the system never enters a deadlock state and further stabilizes in polynomial time. We note that Dijkstra showed that the last problem does not have a deterministic solution even when the identical processors possess an arbitrary power: starting from a ring with a multitude of tokens, any deterministic system will either not stabilize or will enter a deadlock state.

Several distributed algorithms require that there be a coordinator process in the entire system. Since all other processes in the system have to interact with the coordinator, they all must agree on who the coordinator is. Furthermore, if the coordinator process fails due to the failure of the site on which it is located, a new coordinator process must be elected to take up the job of the failed coordinator. Election algorithms are meant for electing a coordinator among currently running processes. This paper deals with the distributed leader election algorithm for a set of processes connected by a tree network. In this paper, we propose a linear time algorithm for leader election using heap structure and describe it in details.

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

We study the time needed for deterministic leader election in the 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 that leader election is impossible otherwise, and weak LE, which differs from strong LE in that no requirement on the behavior of nodes is imposed, if leader election is impossible. We show that the time of leader election depends on three parameters of the network: its diameter D, its size n, and its level of symmetry λ, which, when leader election is feasible, is the smallest depth at which some node has a unique view of the network. It also depends on the knowledge by the nodes, or lack of it, of parameters D and n.

Traditionally, link-state routing (LSR) uses two costly techniques to achieve its robustness and responsiveness: message forwarding on every communication link in the broadcast of network status updates, and the periodic broadcast of local status by every router. In this paper, we present a novel LSR protocol, called Tree-based LSR (T-LSR), which reduces the operational overhead of LSR as follows. A leader router is elected to periodically broadcast network status on behalf of all the other routers in the network, and a spanning tree is constructed to support these broadcasts. The spanning tree is used for most flooding operations, although the protocol reverts to conventional flooding during leader election and spanning tree construction. The T-LSR protocol distinguishes itself from previous tree-based, lightweight LSR methods by its fault-tolerance features: in addition to surviving network partitioning, the T-LSR protocol is shown to maintain consistent routing information and leader preferences throughout the network in the presence of undetected transmission/information corruption problems. The results of a simulation study demonstrate that the T-LSR protocol imposes a small fraction of the overhead of conventional LSR.

In this work, we place a long-established distributed computing problem in a new context. Specifically, the group leader election problem is studied "inside the network," meaning that participants in the election process are network switches/routers, rather than hosts. In this context, an election protocol can take advantage of certain internal operations of the network, such as the underlying routing protocol, to meet stringent fault-tolerance criteria while minimizing the network traffic overhead. A robust solution to the problem, called the Network Leader Election (NLE) protocol, is proposed. The protocol is designed for use in networks based on link-state routing (LSR). The protocol is robust, for it achieves leadership consensus in the presence of adverse events, such as leader failures and network partitioning. The correctness of the protocol is proved formally. A simulation study reveals that the NLE protocol incurs low overhead in handling leader failures and in-group creation. In addition, it is shown how important network functions, including hierarchical routing, address resolution, and multicast core management, can benefit from the NLE protocol.

Traditionally, link-state routing (LSR) uses two costly techniques to achieve its robustness and responsiveness: message forwarding on every communication link in the broadcast of network status updates, and the periodic broadcast of local status by every router. In this paper, we present a novel LSR protocol, called Tree-based LSR (T-LSR), which reduces the operational overhead of LSR as follows. A leader router is elected to periodically broadcast network status on behalf of all the other routers in the network, and a spanning tree is constructed to support these broadcasts. The spanning tree is used for most flooding operations, although the protocol reverts to conventional flooding during leader election and spanning tree construction. The T-LSR protocol distinguishes itself from previous tree-based, lightweight LSR methods by its fault-tolerance features: in addition to surviving network partitioning, the T-LSR protocol is shown to maintain consistent routing information and leader preferences throughout the network in the presence of undetected transmission/information corruption problems. The results of a simulation study demonstrate that the T-LSR protocol imposes a small fraction of the overhead of conventional LSR.

The IEEE 1394 tree identify protocol illustrates the adequacy of the event-driven approach used together with the B Method. This approach provides a complete framework for developing mathematical models of distributed algorithms. A specific development is made of a series of more and more refined models. Each model is made of a number of static properties (the invariant) and dynamic parts (the guarded events). The internal consistency of each model as well as its correctness with regard to its previous abstraction are proved with the proof engine of Atelier B, which is the tool associated with B. In the case of IEEE 1394 tree identify protocol, the initial model is very primitive: it provides the basic properties of the graph (symmetry, acyclicity, connectivity), and its dynamic parts essentially contain a single event which elects the leader in one shot. Further refinements introduce more events, showing how each node of the graph non-deterministically participates in the leader election. At some stage in the development, message passing is introduced. This raises a specific potential contention problem, whose solution is given. The last stage of the refinement completely localises the events by making them take decisions based on local data only.

This paper addresses the problem of distributively electing a leader in both synchronous and asynchronous complete networks. In the synchronous case, we prove a lower bound of ft(n'logn) on the message complexity. We also prove that any message-optimal synchronous algorithm requires ~(log n) time. In proving these bounds we do not restrict the type of operations performed by nodes. The bounds thus apply to general algorithms and not just to comparison based algorithms. A simple algorithm which achieves these bounds is presented. In the asynchronous case, we present a sequence of three simple and efficient algorithms, each of which is an improvement on the previous. The third algorithm has time complexity O(n) and message complexity 2.n.logn+O(n), thus improving the time complexity of the previous best algorithm [Kor84] by a factor of logn. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.

In recent years, there has been a growing interest in wireless sensor networks. One of the major issues in wireless sensor network is developing an energy-efficient clustering protocol. Hierarchical clustering algorithms are very important in increasing the network's life time. Each clustering algorithm is composed of two phases, the setup phase and steady state phase. The hot point in these algorithms is the cluster head selection. In this paper, we study the impact of heterogeneity of nodes in terms of their energy in wireless sensor networks that are hierarchically clustered. We assume that a percentage of the population of sensor nodes is equipped with the additional energy resources. We also assume that the sensor nodes are randomly distributed and are not mobile, the coordinates of the sink and the dimensions of the sensor field are known. Homogeneous clustering protocols assume that all the sensor nodes are equipped with the same amount of energy and as a result, they cannot take the advantage of the presence of node heterogeneity. Adapting this approach, we introduce an energy efficient heterogeneous clustered scheme for wireless sensor networks based on weighted election probabilities of each node to become a cluster head according to the residual energy in each node. Finally, the simulation results demonstrate that our proposed heterogeneous clustering approach is more effective in prolonging the network lifetime compared with LEACH.

Tracking is one of the major applications of wireless sensor networks. EnviroSuite, as a programming paradigm, provides a comprehensive solution for programming tracking applications, wherein moving environmental targets are uniquely and identically mapped to logical objects to raise the level of programming abstraction. Such mapping is done through distributed group management algorithms, which organize nodes in the vicinity of targets into groups, and maintain the uniqueness and identity of target representation such that each target is given a consistent name. Challenged by tracking fast-moving targets, this paper explores, in a systematic way, various group management optimizations including semi-dynamic leader election, piggy-backed heartbeats, and implicit leader election. The resulting tracking protocol, Lightweight Envi-roSuite, is integrated into a surveillance system. Empirical performance evaluation on a network of 200 XSM motes shows that, due to these optimizations, Lightweight EnviroSuite is able to track targets more than 3 times faster than the fastest targets trackable by the original EnviroSuite even when 20% of nodes fail.

We i n v estigate the problem of self-stabilizing round-robin token management s c heme on an anonymous bidirectional ring of identical processors, where each processor is an asynchronous probabilistic coin-ipping nite state machine which sends and receives messages. We show that the solution to this problem is equivalent to symmetry breaking i.e., leader election. Requiring only constant-size messages and message-passing model has practical implications: our solution can be implemented in high-speed networks using a universal fast hardware switches i.e., nite state machines of size independent of the size of the network. Our automata-based message-passing model has inherent deadlock possibility i.e., when all processors are waiting for a message which w e assume is detected by an external timeout mechanism. Provided that there is no deadlock to begin with, we show h o w starting from an arbitrary con guration, the system never enters a deadlock state and further stabilizes in polynomial time. We note that Dijkstra showed that the last problem does not have a deterministic solution even when the identical processors possess an arbitrary power: starting from a ring with a multitude of tokens, any deterministic system will either not stabilize or will enter a deadlock state.

Leader election algorithms (LEAs) solve the instability problem in the network, which caused by leader failure. Dynamic LEAs solve some problems that appear during algorithm execution. One of the major problems affect the completion of the algorithm is intermittent or complete links failure. This research concerns in building and designing a dynamic leader election algorithm, to contribute in solving leader failure problem in two dimensional torus network despite the existing of complete or intermittent links failure. . In two dimensional torus network with connected N nodes and F failed links, the proposed algorithm needs O (N+F) messages in time steps to complete the election process.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Biographical NoteThomas Andrew Daschle was born on December 9, 1947, in Aberdeen, South Dakota, to Elizabeth B. Meier and Sebastian C. Daschle. He attended South Dakota State University, being graduated with a degree in political science in 1969. After college he served as an intelligence officer in the U.S. Air Force. He started in politics as a staff member to

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, . . . , d -1. Colored networks are generalizations both of labeled networks, in which nodes have distinct labels, and of anonymous networks, in which nodes do not have labels (all nodes have the same color). In colored networks, topology recognition and leader election are not always feasible. Hence we study two more general problems. Consider a colored network and an input I given to its nodes. The aim of the problem TOP, for this colored network and for I, is to solve topology recognition in this network, if this is possible under input I, and to have all nodes answer "unsolvable" otherwise. Likewise, the aim of the problem LE is to solve leader election in this network, if this is possible under input I, and to have all nodes answer "unsolvable" otherwise. We show that nodes of a network can solve problems TOP and LE, if they are given, as input I, an upper bound k on the number of nodes of a given color, called the size of this color. On the other hand we show that, if the nodes are given an input that does not bound the size of any color, then the answer to TOP and LE must be "unsolvable", even for the class of rings. Under the assumption that nodes are given an upper bound k on the size of a given color, we study the time of solving problems TOP and LE in the LOCAL model in which, during each round, each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. We give an algorithm to solve each of these problems in arbitrary networks in time O(kD + D log(n/D)), where D is the diameter of the network and n is its size. We also show that this time is optimal, by exhibiting classes of networks in which every algorithm solving problems TOP or LE must use time Ω(kD + D log(n/D)).

Leader election is one of the basic problems in distributed computing. This is a symmetry breaking problem: all nodes of a network must agree on a single node, called the leader. If the nodes of the network have distinct labels, then such an agreement means that all nodes have to output the label of the elected leader. 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 numbers, such that all these paths end at a common node, the leader. In this paper, we study deterministic leader election in arbitrary anonymous networks. It is well known that leader election is impossible in some networks, regardless of the allocated amount of time, even if nodes know the map of the network. This is due to possible symmetries in it. However, even in networks in which it is possible to elect a leader knowing the map, the task may be still impossible without any knowledge, regardless of the allocated time. On the other hand, for any network in which leader election is possible knowing the map, there is a minimum time, called the election index, in which this can be done. Informally, the election index of a network is the minimum depth at which views of all nodes are distinct. Our aim is to establish tradeoffs between the allocated time τ and the amount of information that has to be given a priori to the nodes to enable leader election in time τ in all networks for which leader election in this time is at all possible. Following the framework of algorithms with advice, this information (a single binary string) is provided to all nodes at the start by an oracle knowing the entire network. The length of this string is called the size of advice. For a given time τ allocated to leader election, we give upper and lower bounds on the minimum size of advice sufficient to perform leader election in time τ . We focus on the two sides of the time spectrum. For the smallest possible time, which is the election index of the network, we show that the minimum size of advice is linear in the size n of the network, up to polylogarithmic factors. On the other hand, we consider large values of time: larger than the diameter D by a summand, respectively, linear, polynomial, and exponential in the election index; for these values, we prove tight bounds on the minimum size of advice, up to multiplicative constants. We also show that constant advice is not sufficient for leader election in all graphs, regardless of the allocated time.

The Election protocol can be used as a building block in many practical problems such as group communication, atomic commit and replicated data management where a protocol coordinator might be useful. The problem has been widely studied in the research community since one reason for this wide interest is that many distributed protocols need an election protocol. However, despite its usefulness, to our knowledge there is no work that has been devoted to this problem in a mobile computing environment. Mobile systems are more prone to failures than conventional distributed systems. Solving election in such an environment requires from a set of mobile hosts to choose a mobile host or a fixed host based on the their priority despite failures of both mobile computing and/or fixed hosts. In this paper, we describe a solution to the election problem from mobile computing systems. This solution is based on the Garcia Molina's Bully algorithm.

Probabilistic algorithms are designed to handle problems that do not admit deterministic effective solutions. In the case of the election problem, many algorithms are available and applicable under appropriate assumptions, for example: the uniform election in trees, k-trees and polyominoids. In this paper, first, we introduce a probabilistic algorithm for the uniform election in the triangular grid graphs, then, we expose the set of rules that generate the class of the triangular grid graphs. The main of this paper is devoted to the analysis of our algorithm. We show that our algorithm is totally fair in so far as it gives the same probability to any vertex of the given graph to be elected.

We propose a dynamic distributed algorithm for tracking objects that move fast in a sensor network. In the earlier efforts in tracking moving targets, the current leader node at time t predicts the location only for time t 1 1 and if the target moves in high speed, it can pass by a group of nodes very fast without being detected. Therefore, as the target increases its speed, the probability of missing that target also increases. In this study, we propose a target tracking system that predicts future k locations of the target and awakens the corresponding leader nodes so that the nodes along the trajectory self organize to form the clusters to collect data related to the target in advance and thus reduce the target misses. The algorithm first provides detection of the target and forms a cluster with the neighboring nodes around it. After the selection of the cluster leader, the coordinates of the target is estimated using localization methods and cooperation between the cluster nodes under the control of the leader node. The coordinates and the speed of the target are then used to estimate its trajectory. This information in turn provides the location of the nodes along the estimated trajectory which can be awaken, hence providing tracking of the moving object. We describe the algorithm, analyze its efficiency and show by simulations that it performs well to track very fast moving objects with speeds much higher than reported in literature.

This paper studies a variant of the leader election problem under the stone age model (Emek and Wattenhofer, PODC 2013) that considers a network of n randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the beeping model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as k-leader selection, in which a leader should be selected out of at most k initial candidates. Our main contribution is an algorithm that solves k-leader selection for bounded k in the aforementioned stone age model. On (general topology) graphs of diameter D, this algorithm runs inÕ(D) time and succeeds with high probability. The assumption that k is bounded turns out to be unavoidable: we prove that if k = ω(1), then no algorithm in this model can solve k-leader selection with a (positive) constant probability.

This paper studies a variant of the \emph{leader election} problem under the \emph{stone age} model (Emek and Wattenhofer, PODC 2013) that considers a network of $n$ randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the \emph{beeping} model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as \emph{$k$-leader selection}, in which a leader should be selected out of at most $k$ initial candidates. Our main contribution is an algorithm that solves $k$-leader selection for bounded $k$ in the aforementioned stone age model. On (general topology) graphs of diameter $D$, this algorithm runs in $\tilde{O}(D)$ time and succeeds with high probability. The assumption that $k$ is bounded turns out to be unavoidable: we prove that if $k = \omega (1)$, then no algorithm in this model can solve $k$-leader selection ...

We introduce a temporal logic to reason on global applications in an asynchronous setting. First, we define the Distributed States Logic (DSL), a modal logic for localities that embeds the local theories of each component into a theory of the distributed states of the system. We provide the logic with a sound and complete axiomatization. The contribution is that it is possible to reason about properties that involve several components, even in the absence of a global clock. Then, we define the Distributed States Temporal Logic (DSTL) by introducing temporal operators a' la Unity. We support our proposal by working out a pair of examples: a simple secure communication system, and an algorithm for distributed leader election. The motivation for this work is that the existing logics for distributed systems do not have the right expressive power to reason on the systems behaviour, when the communication is based on asynchronous message passing. On the other side, asynchronous commun...

With the proliferation of portable computing platforms and small wireless devices, the classical dilemma of leader election in mobile ad hoc networks has received attention from the research community in recent years. The problem aims to elect a unique leader among mobile nodes regardless of their physical locations. But, existing distributed leader election algorithms do not cope with highly spontaneous nature of mobile ad hoc networks. This paper presents a consensus-based leader election algorithm that finds a local extrema among the nodes participating in leader election. The algorithm is highly adaptive with ad hoc networks in the sense that it can tolerate intermittent failures, such as link failures, sudden crash or recovery of mobile nodes, network partitions, and merging of connected network components associated with ad hoc networks. The paper also presents proofs of correctness to exhibit the fairness of this algorithm.

The process of electing the master node in distributed systems is a common problem that requires a huge amount of time. To participate in solving such problem, this research paper presents an improvement version for bully algorithm which bases on clustering concept. The proposed framework divided the distributed system into main cluster and sub cluster, in which the main consists of master and assistant nodes, while sub cluster holds Demaster, Assistant nodes and leaf nodes. The constructed framework reduced the communications overload and single point of failure.

Leader election algorithms (LEAs) solve the instability problem in the network, which caused by leader failure. Dynamic LEAs solve some problems that appear during algorithm execution. One of the major problems affect the completion of the algorithm is intermittent or complete links failure. This research concerns in building and designing a dynamic leader election algorithm, to contribute in solving leader failure problem in two dimensional torus network despite the existing of complete or intermittent links failure.. In two dimensional torus network with connected N nodes and F failed links, the proposed algorithm needs O (N+F) messages in time steps to complete the election process.

A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node. Agents are anonymous (identical), execute the same deterministic algorithm and move in synchronous rounds along links of the network. An initial configuration of agents is called gatherable if there exists a deterministic algorithm (even dedicated to this particular configuration) that achieves meeting of all agents in one node. Which configurations are gatherable and how to gather all of them deterministically by the same algorithm? We give a complete solution of this gathering problem in arbitrary networks. We characterize all gatherable configurations and give two universal deterministic gathering algorithms, i.e., algorithms that gather all gatherable configurations. The first algorithm works under the assumption that a common upper bound N on the size of the network is known to all agents. In this case our algorithm guarantees gathering with detection, i.e., the existence of a round for any gatherable configuration, such that all agents are at the same node and all declare that gathering is accomplished. If no upper bound on the size of the network is known, we show that a universal algorithm for gathering with detection does not exist. Hence, for this harder scenario, we construct a second universal gathering algorithm, which guarantees that, for any gatherable configuration, all agents eventually get to one node and stop, although they cannot tell if gathering is over. The time of the first algorithm is polynomial in the upper bound N on the size of the network, and the time of the second algorithm is polynomial in the (unknown) size itself. Our results have an important consequence for the leader election problem for anonymous agents in arbitrary graphs. Leader election is a fundamental symmetry breaking problem in distributed computing. Its goal is to assign, in some common round, value 1 (leader) to one of the entities and value 0 (nonleader) to all others. For anonymous agents in graphs, leader election turns out to be equivalent to gathering with detection. Hence, as a by-product, we obtain a complete solution of the leader election problem for anonymous agents in arbitrary graphs.

Two mobile agents starting at different nodes of an unknown network have to meet. This task is known in the literature as rendezvous. Each agent has a different label which is a positive integer known to it, but unknown to the other agent. Agents move in an asynchronous way: the speed of agents may vary and is controlled by an adversary. The cost of a rendezvous algorithm is the total number of edge traversals by both agents until their meeting. The only previous deterministic algorithm solving this problem has cost exponential in the size of the graph and in the larger label. In this paper we present a deterministic rendezvous algorithm with cost polynomial in the size of the graph and in the length of the smaller label. Hence we decrease the cost exponentially in the size of the graph and doubly exponentially in the labels of agents. As an application of our rendezvous algorithm we solve several fundamental problems involving teams of unknown size larger than 1 of labeled agents moving asynchronously in unknown networks. Among them are the following problems: team size, in which every agent has to find the total number of agents, leader election, in which all agents have to output the label of a single agent, perfect renaming in which all agents have to adopt new different labels from the set {1,. .. , k}, where k is the number of agents, and gossiping, in which each agent has initially a piece of information (value) and all agents have to output all the values. Using our rendezvous algorithm we solve all these problems at cost polynomial in the size of the graph and in the smallest length of all labels of participating agents.

Leader election is one of the basic problems in distributed computing. This is a symmetry breaking problem: all nodes of a network must agree on a single node, called the leader. If the nodes of the network have distinct labels, then such an agreement means that all nodes have to output the label of the elected leader. 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 numbers, such that all these paths end at a common node, the leader. In this paper, we study deterministic leader election in arbitrary anonymous networks. It is well known that leader election is impossible in some networks, regardless of the allocated amount of time, even if nodes know the map of the network. This is due to possible symmetries in it. However, even in networks in which it is possible to elect a leader knowing the map, the task may be still impossible without any knowledge, regardless of the allocated time. On the other hand, for any network in which leader election is possible knowing the map, there is a minimum time, called the election index, in which this can be done. Informally, the election index of a network is the minimum depth at which views of all nodes are distinct. Our aim is to establish tradeoffs between the allocated time τ and the amount of information that has to be given a priori to the nodes to enable leader election in time τ in all networks for which leader election in this time is at all possible. Following the framework of algorithms with advice, this information (a single binary string) is provided to all nodes at the start by an oracle knowing the entire network. The length of this string is called the size of advice. For a given time τ allocated to leader election, we give upper and lower bounds on the minimum size of advice sufficient to perform leader election in time τ. We focus on the two sides of the time spectrum. For the smallest possible time, which is the election index of the network, we show that the minimum size of advice is linear in the size n of the network, up to polylogarithmic factors. On the other hand, we consider large values of time: larger than the diameter D by a summand, respectively, linear, polynomial, and exponential in the election index; for these values, we prove tight bounds on the minimum size of advice, up to multiplicative constants. We also show that constant advice is not sufficient for leader election in all graphs, regardless of the allocated time.

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 leader election in anonymous trees. Our goal is to establish tradeoffs between the allocated time τ and the amount of information that has to be given a priori to the nodes of a network to enable leader election in time τ. Following the framework of algorithms with advice, this information is provided to all nodes at the start by an oracle knowing the entire tree, in form of binary strings assigned to all nodes. There are two possible variants of formulating this advice assignment. Either the strings provided to all nodes are identical, or strings assigned to different nodes may be potentially different, i.e., advice can be customized. As opposed to previous papers on leader election with advice, in this paper we consider the latter option. The maximum length of all assigned binary strings is called the size of advice. For a given time τ allocated to leader election, we give upper and lower bounds on the minimum size of advice sufficient to perform leader election in time τ. All our bounds except one pair are tight up to multiplicative constants, and in this one exceptional case, the gap between the upper and the lower bound is very small.

A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node. Agents are anonymous (identical), execute the same deterministic algorithm and move in synchronous rounds along links of the network. An initial configuration of agents is called gatherable if there exists a deterministic algorithm (even dedicated to this particular configuration) that achieves meeting of all agents in one node. Which configurations are gatherable and how to gather all of them deterministically by the same algorithm? We give a complete solution of this gathering problem in arbitrary networks. We characterize all gatherable configurations and give two universal deterministic gathering algorithms, i.e., algorithms that gather all gatherable configurations. The first algorithm works under the assumption that a common upper bound N on the size of the network is known to all agents. In this case our algorithm guarantees gathering with detection, i.e., the existence of a round for any gatherable configuration, such that all agents are at the same node and all declare that gathering is accomplished. If no upper bound on the size of the network is known, we show that a universal algorithm for gathering with detection does not exist. Hence, for this harder scenario, we construct a second universal gathering algorithm, which guarantees that, for any gatherable configuration, all agents eventually get to one node and stop, although they cannot tell if gathering is over. The time of the first algorithm is polynomial in the upper bound N on the size of the network, and the time of the second algorithm is polynomial in the (unknown) size itself. Our results have an important consequence for the leader election problem for anonymous agents in arbitrary graphs. Leader election is a fundamental symmetry breaking problem in distributed computing. Its goal is to assign, in some common round, value 1 (leader) to one of the entities and value 0 (nonleader) to all others. For anonymous agents in graphs, leader election turns out to be equivalent to gathering with detection. Hence, as a by-product, we obtain a complete solution of the leader election problem for anonymous agents in arbitrary graphs.

Mobile Ad-hoc Network is a peer-to-peer wireless network that transmits data from computer to computer without the use of a central base station or access point. Intrusion detection techniques are used for the network attack detection process. The system is designed to handle leader election scheme for intrusion detection process. In this paper, we use leader election algorithm to find the globally optimal cost-efficient leader and it is devised to handle the election process for possibility of cheating and security flaws, such as replay attacks. The clustering scheme is optimized with coverage and traffic level. Cost and resource utilization is controlled under the clusters. The system development and analysis are carried out under the JiST (Java in Simulation Time) simulation environment.

How to pass from local to global scales in anonymous networks? In such networks, how to organize a self-stabilizing propagation of information with feedback? From Angluin's results, the deterministic leader election is impossible in general anonymous networks. Thus, it is impossible to build a rooted spanning tree. In this paper we show how to use Unison to design a self- stabilizing barrier synchronization in an anonymous network. We show that the communication structure of this barrier synchronization designs a self-stabilizing wave stream, or pipelined wave, in anonymous networks. We introduce two variants of waves: Strong Wave and Wavelet. Strong waves can be used to solve the idempotent r-operator parametrized problem, which implies well known problems like depth-first search tree construction - this instance requires identities for the processors. Wavelets deal with ρ-distance computation. We show how to use Unison to design a self-stabilizing strong wave stream, and wave...

A leader node in Ad hoc networks and especially in WSNs and IoT networks is needed in many cases, for example to generate keys for encryption/decryption, to find a node with minimum energy or situated in an extreme part of the network. In our work, we need as a leader the node situated on the extreme left of the network to start the process of finding its boundary nodes. These nodes will be used to monitor any sensitive, dangerous or non-accessible site. For this kind of applications, algorithms must be robust and fault-tolerant since it is difficult and even impossible to intervene if a node fails. Such a situation can be catastrophic in case that this node is the leader. In this paper, we present a new algorithm called DoTRo, which is based on a tree routing protocol. It starts from local leaders which will start the process of flooding to determine a spanning tree. During this process their value will be routed. If two spanning trees meet each other then the tree routing the best value will continue its process while the other tree will stop it. The remaining tree is the dominating one and its root will be the leader. This algorithm turns out to be low energy consuming with reduction rates that can exceed 85%. It is efficient and fault-tolerant since it works in the case where any node can fail and in the case where the network is disconnected.

This paper presents an algorithm for flexible and fast leader election in distributed systems using Apache Zookeeper for configuration management. The algorithm proposed in this paper is designed for applications that do not use symmetric nodes so they need a specialized election process or for applications that require a more flexible approach in the leader election process. The algorithm proposes a different approach as it allows assigning prioritizations for servers in the cluster that are candidates to become a leader. The algorithm is flexible as it takes into consideration during the leader election process of the different server settings and roles, network properties, communication latency or specific application requirements.

We provide the first quantum (exact) protocol for the Dining Philosophers problem (DP), a central problem in distributed algorithms. It is well known that the problem cannot be solved exactly in the classical setting. We then use our DP protocol to provide a new quantum protocol for the tightly related problem of exact leader election (LE) on a ring, improving significantly in both time and memory complexity over the known LE protocol by Tani et. al. To do this, we show that in some sense the exact DP and exact LE problems are equivalent; interestingly, in the classical non-exact setting they are not. Hopefully, the results will lead to exact quantum protocols for other important distributed algorithmic questions; in particular, we discuss interesting connections to the ring size problem, as well as to a physically motivated question of breaking symmetry in 1D translationally invariant systems.

We present distributed protocols for electing a leader among k mobile agents that are dispersed among the n nodes of a graph. While previous solutions for the agent election problem were restricted to specific topologies or under specific conditions, the protocols presented in this paper face the problem in the most general case, i.e. for an arbitrary topology where the nodes of the graph may not be distinctly labelled and the agents might be all identical (and thus indistinguishable from each other). In such cases, the agent election problem is often difficult, and sometimes impossible to solve using deterministic means. We have designed protocols for solving the problem that-unlike previous solutions-are effective, meaning that they always succeed in electing a leader under any given setting if at all it is possible, and otherwise detect the fact that election is impossible in that setting. We present several election protocols, all effective. Starting with the straightforward solution, that requires an exponential amount of edge-traversals by the agents, we describe significantly more efficient algorithms; in the latter the total number of edge-traversals made by the agents is always polynomial, their difference is in the amount of bits of storage they required at the nodes.

We consider a distributed version of the graph exploration and mapping problem where a mobile agent has to traverse the edges of an unlabelled (i.e., anonymous) graph and return to its starting point, building a map of the graph in the process. In our case, instead of a single agent, there are k identical (i.e., mutually indistinguishable) agents initially dispersed among the n nodes of the graph. The agents can communicate by writing to the small public bulletin boards available at each node. The objective is for each agent to build an identically labelled map of the graph; we call this the Labelled Map Construction problem. This problem is much more difficult than exploration by a single agent, because it involves achieving cooperation among multiple agents. In fact, this problem is deterministically unsolvable in some cases. We present deterministic algorithms that successfully and efficiently solve the problem under the condition that the values of n and k are co-prime with each other. We also show how the problem of Labelled Map Construction is related to other problems like leader election and rendezvous of agents.

We analyze further the Magnus-Derek game, a two-player game played on a round table with n positions. The players jointly control the movement of a token. One player, Magnus, aims to maximize the number of positions visited while minimizing the number of rounds. The other player, Derek, attempts to minimize the number of visited positions. We present a new strategy for Magnus that succeeds in visiting the maximal number of positions in 3(n − 1) rounds, which is the optimal number of rounds up to a constant factor.