Robust Leader Election in a Fast-Changing World

2007

Radio networks (RN) are distributed systems (ad hoc networks) consisting in n ≥ 2 radio stations. Assuming the number n unknown, two distinct models of RN without collision detection (no-CD) are addressed: the model with weak no-CD RN and the one with strong no-CD RN. We design and analyze two distributed leader election protocols, each one running in each of the above two (no-CD RN) models, respectively. Both randomized protocols are shown to elect a leader within O(log (n)) expected time, with no station being awake for more than O(log log (n)) time slots (such algorithms are said to be energy-efficient). Therefore, a new class of efficient algorithms is set up that match the Ω(log (n)) time lower-bound established by Kushilevitz and Mansour in [11].

Proceedings of the 20th International Conference on Advanced Information Networking and Applications, 2006

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.

Lecture Notes in Computer Science, 2016

This paper presents a distributed algorithm, called ST T , 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). In fact, using the lower bound by Kutten et al. [13] and a result of Dinitz and Solomon [8], we show that the bit round complexity of ST T is optimal (up to a constant factor), which is a step forward in understanding the interplay between time and message optimality for the election problem. Our algorithm requires no knowledge on the graph such as n or D.

Unlike the well-studied cellular networks that assume the existence o robust infrastructure, Ad-hoc Networks (AHN, for short) are rapidly deplo able, self-organizing, and do not rely on an existing infrastructure. These ne works find applications to disaster-relief, search-and-rescue, law-enforcem and collaborative computing, among others.

Leader election is a very important problem, not only in wired networks, but in mobile, ad hoc networks as well. Existing solutions to leader election do not handle frequent topology changes and dynamic nature of mobile networks. In this paper, we present a leader election algorithm that is highly adaptive to arbitrary (possibly concurrent) topological changes and is therefore well-suited for use in mobile ad hoc networks. The algorithm is based on finding an extrema and uses diffusing computations for this purpose. We show, using linear-time temporal logic, that the algorithm is "weakly" self-stabilizing and terminating. We also simulate the algorithm in a mobile ad hoc setting. Through our simulation study, we elaborate on several important issues that can significantly impact performance of such a protocol for mobile ad hoc networks such as choice of signaling, broadcast nature of wireless medium etc. Our simulation study shows that our algorithm is quite effective in that each node has a leader approximately 97-99% of the time in a variety of operating conditions.

Distributed Computing, 2019

This paper focuses on studying the message complexity of implicit leader election in synchronous distributed networks of diameter two. Kutten et al. (J ACM 62(1):7:1-7:27, 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. (Theor Comput Sci 561(Part B):134-143, 2015) established a tight bound ofΘ(√ n) on the message complexity of randomized leader election (n is the number of nodes in the network). For graphs of diameter two, the complexity was not known. In this paper, we settle this complexity by showing a tight bound ofΘ(n) on the message complexity of leader election in diameter-two networks. We first give a simple randomized Monte-Carlo leader election algorithm that with high probability (i.e., probability at least 1 − n −c , for some fixed positive constant c) succeeds and uses O(n log 3 n) messages and runs in O(1) rounds; this algorithm works without knowledge of n (and hence needs no global knowledge). We then show that any algorithm (even Monte Carlo randomized algorithms with large enough constant success probability) needs Ω(n) messages (even when n is known), regardless of the number of rounds. We also present an O(n log n) message deterministic algorithm that takes O(log n) rounds (but needs knowledge of n); we show that this message complexity is tight for deterministic algorithms. Together with the two previous results of Kutten et al., our results fully characterize the message complexity of leader election vis-à-vis the graph diameter.

Lecture Notes in Computer Science, 2012

We consider the task of electing a leader in a distributed manner in ad hoc multi-hop radio networks. Radio networks represent the class of wireless networks in which one frequency is used for transmissions, network's topology can be represented by a simple undirected graph with some n nodes, and there is no collision detection. We give a randomized algorithm electing a leader in O(n) expected time and prove that this time bound is optimal. We give a deterministic algorithm electing a leader in O(n log 3/2 n √ log log n) time. By way of application, we show how to perform gossiping with combined messages in O(n log 3/2 n √ log log n) time by a deterministic algorithm, and in O(n) expected time by a randomized algorithm.

Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures, 2020

Leader election is a fundamental task in distributed computing. It is a symmetry breaking problem, calling for one node of the network to become the leader, and for all other nodes to become non-leaders. We consider leader election in anonymous radio networks modeled as simple undirected connected graphs. Nodes communicate in synchronous rounds. In each round, a node can either transmit a message to all its neighbours, or stay silent and listen. A node v hears a message from a neighbour w in a given round if v listens in this round and if w is its only neighbour transmitting in this round. If v listens in a round in which more than one neighbour transmits then v hears noise that is different from any message and different from silence. We assume that nodes are identical (anonymous) and execute the same deterministic algorithm. Under this scenario, 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...

Information and Computation, 2007

Radio networks (RN) are distributed systems (ad hoc networks) consisting in n ≥ 2 radio stations. Assuming the number n unknown, two distinct models of RN without collision detection (no-CD) are addressed: the model with weak no-CD RN and the one with strong no-CD RN. We design and analyze two distributed leader election protocols, each one running in each of the above two (no-CD RN) models, respectively. Both randomized protocols are shown to elect a leader within O(log (n)) expected time, with no station being awake for more than O(log log (n)) time slots (such algorithms are said to be energy-efficient). Therefore, a new class of efficient algorithms is set up that match the Ω(log (n)) time lower-bound established by Kushilevitz and Mansour in [11].

ACM Transactions on Algorithms, 2022

Leader election is a fundamental task in distributed computing. It is a symmetry breaking problem, calling for one node of the network to become the leader , and for all other nodes to become non-leaders . We consider leader election in anonymous radio networks modeled as simple undirected connected graphs. Nodes communicate in synchronous rounds. In each round, a node can either transmit a message to all its neighbours, or stay silent and listen. A node v hears a message from a neighbour w in a given round if v listens in this round and if w is its only neighbour transmitting in this round. If v listens in a round in which more than one neighbour transmits then v hears noise that is different from any message and different from silence. We assume that nodes are identical (anonymous) and execute the same deterministic algorithm. Under this scenario, 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 a...