Robust Leader Election in a Fast-Changing World

We consider the problem of electing a leader among nodes in a highly dynamic network where the adversary has unbounded capacity to insert and remove nodes (including the leader) from the network and change connectivity at will. We present a randomized Las Vegas algorithm that (re)elects a leader in O(D\log n) rounds with high probability, where D is a bound on the dynamic diameter of the network and n is the maximum number of nodes in the network at any point in time. We assume a model of broadcast-based communication where a node can send only 1 message of O(\log n) bits per round and is not aware of the receivers in advance. Thus, our results also apply to mobile wireless ad-hoc networks, improving over the optimal (for deterministic algorithms) O(Dn) solution presented at FOMC 2011. We show that our algorithm is optimal by proving that any randomized Las Vegas algorithm takes at least omega(D\log n) rounds to elect a leader with high probability, which shows that our algorithm yields the best possible (up to constants) termination time.Comment: In Proceedings FOMC 2013, arXiv:1310.459

Faster Gossiping in Bidirectional Radio Networks with Large Labels

We consider unknown ad-hoc radio networks, when the underlying network is bidirectional and nodes can have polynomially large labels. For this model, we present a deterministic protocol for gossiping which takes $O(n \lg^2 n \lg \lg n)$ rounds. This improves upon the previous best result for deterministic gossiping for this model by [Gasienec, Potapov, Pagourtizis, Deterministic Gossiping in Radio Networks with Large labels, ESA (2002)], who present a protocol of round complexity $O(n \lg^3 n \lg \lg n)$ for this problem. This resolves open problem posed in [Gasienec, Efficient gossiping in radio networks, SIROCCO (2009)], who cite bridging gap between lower and upper bounds for this problem as an important objective. We emphasize that a salient feature of our protocol is its simplicity, especially with respect to the previous best known protocol for this problem

Two algorithms for leader election and network size estimation in mobile ad hoc networks

We develop two algorithms for important problems in mobile ad hoc networks (MANETs). A MANET is a collection of mobile processors (nodes) which communicate via message passing over wireless links. Each node can communicate directly with other nodes within a specified transmission radius; other communication is accomplished via message relay. Communication links may go up and down in a MANET (as nodes move toward or away from each other); thus, the MANET can consist of multiple connected components, and connected components can split and merge over time. We first present a deterministic leader election algorithm for asynchronous MANETs along with a correctness proof for it. Our work involves substantial modifications of an existing algorithm and its proof, and we adapt the existing algorithm to the asynchronous environment. Our algorithms running time and message complexity compare favorably with existing algorithms for leader election in MANETs. Second, many algorithms for MANETs require or can benefit from knowledge about the size of the network in terms of the number of processors. As such, we present an algorithm to approximately determine the size of a MANET. While the algorithms approximations of network size are only rough ones, the algorithm has the important qualities of requiring little communication overhead and being tolerant of link failures

Self-stabilizing leader election in dynamic networks

The leader election problem is one of the fundamental problems in distributed computing. It has applications in almost every domain. In dynamic networks, topology is expected to change frequently. An algorithm A is self-stabilizing if, starting from a completely arbitrary configuration, the network will eventually reach a legitimate configuration. Note that any self-stabilizing algorithm for the leader election problem is also an algorithm for the dynamic leader election problem, since when the topology of the network changes, we can consider that the algorithm is starting over again from an arbitrary state. There are a number of such algorithms in the literature which require large memory in each process, or which take O(n) time to converge, where n is size of the network. Given the need to conserve time, and possibly space, these algorithms may not be practical for the dynamic leader election problem. In this thesis, three silent self-stabilizing asynchronous distributed algorithms are given for the leader election problem in a dynamic network with unique IDs, using the composite model of computation. If topological changes to the network pause, a leader is elected for each component. A BFS tree is also constructed in each component, rooted at the leader. When another topological change occurs, leaders are then elected for the new components. This election takes O (Diam) rounds, where Diam is the maximum diameter of any component. The three algorithms differ in their leadership stability. The first algorithm, which is the fastest in the worst case, chooses an arbitrary process as the leader. The second algorithm chooses the process of highest priority in each component, where priority can be defined in a variety of ways. The third algorithm has the strictest leadership stability; if a component contains processes that were leaders before the topological change, one of those must be elected to be the new leader. Formal algorithms and their correctness proofs will be given

Byzantine fault-tolerant agreement protocols for wireless Ad hoc networks

Tese de doutoramento, Informática (Ciências da Computação), Universidade de Lisboa, Faculdade de Ciências, 2010.The thesis investigates the problem of fault- and intrusion-tolerant consensus in resource-constrained wireless ad hoc networks. This is a fundamental problem in distributed computing because it abstracts the need to coordinate activities among various nodes. It has been shown to be a building block for several other important distributed computing problems like state-machine replication and atomic broadcast. The thesis begins by making a thorough performance assessment of existing intrusion-tolerant consensus protocols, which shows that the performance bottlenecks of current solutions are in part related to their system modeling assumptions. Based on these results, the communication failure model is identified as a model that simultaneously captures the reality of wireless ad hoc networks and allows the design of efficient protocols. Unfortunately, the model is subject to an impossibility result stating that there is no deterministic algorithm that allows n nodes to reach agreement if more than n2 omission transmission failures can occur in a communication step. This result is valid even under strict timing assumptions (i.e., a synchronous system). The thesis applies randomization techniques in increasingly weaker variants of this model, until an efficient intrusion-tolerant consensus protocol is achieved. The first variant simplifies the problem by restricting the number of nodes that may be at the source of a transmission failure at each communication step. An algorithm is designed that tolerates f dynamic nodes at the source of faulty transmissions in a system with a total of n 3f + 1 nodes. The second variant imposes no restrictions on the pattern of transmission failures. The proposed algorithm effectively circumvents the Santoro- Widmayer impossibility result for the first time. It allows k out of n nodes to decide despite dn 2 e(nk)+k2 omission failures per communication step. This algorithm also has the interesting property of guaranteeing safety during arbitrary periods of unrestricted message loss. The final variant shares the same properties of the previous one, but relaxes the model in the sense that the system is asynchronous and that a static subset of nodes may be malicious. The obtained algorithm, called Turquois, admits f < n 3 malicious nodes, and ensures progress in communication steps where dnf 2 e(n k f) + k 2. The algorithm is subject to a comparative performance evaluation against other intrusiontolerant protocols. The results show that, as the system scales, Turquois outperforms the other protocols by more than an order of magnitude.Esta tese investiga o problema do consenso tolerante a faltas acidentais e maliciosas em redes ad hoc sem fios. Trata-se de um problema fundamental que captura a essência da coordenação em actividades envolvendo vários nós de um sistema, sendo um bloco construtor de outros importantes problemas dos sistemas distribuídos como a replicação de máquina de estados ou a difusão atómica. A tese começa por efectuar uma avaliação de desempenho a protocolos tolerantes a intrusões já existentes na literatura. Os resultados mostram que as limitações de desempenho das soluções existentes estão em parte relacionadas com o seu modelo de sistema. Baseado nestes resultados, é identificado o modelo de falhas de comunicação como um modelo que simultaneamente permite capturar o ambiente das redes ad hoc sem fios e projectar protocolos eficientes. Todavia, o modelo é restrito por um resultado de impossibilidade que afirma não existir algoritmo algum que permita a n nós chegaram a acordo num sistema que admita mais do que n2 transmissões omissas num dado passo de comunicação. Este resultado é válido mesmo sob fortes hipóteses temporais (i.e., em sistemas síncronos) A tese aplica técnicas de aleatoriedade em variantes progressivamente mais fracas do modelo até ser alcançado um protocolo eficiente e tolerante a intrusões. A primeira variante do modelo, de forma a simplificar o problema, restringe o número de nós que estão na origem de transmissões faltosas. É apresentado um algoritmo que tolera f nós dinâmicos na origem de transmissões faltosas em sistemas com um total de n 3f + 1 nós. A segunda variante do modelo não impõe quaisquer restrições no padrão de transmissões faltosas. É apresentado um algoritmo que contorna efectivamente o resultado de impossibilidade Santoro-Widmayer pela primeira vez e que permite a k de n nós efectuarem progresso nos passos de comunicação em que o número de transmissões omissas seja dn 2 e(n k) + k 2. O algoritmo possui ainda a interessante propriedade de tolerar períodos arbitrários em que o número de transmissões omissas seja superior a . A última variante do modelo partilha das mesmas características da variante anterior, mas com pressupostos mais fracos sobre o sistema. Em particular, assume-se que o sistema é assíncrono e que um subconjunto estático dos nós pode ser malicioso. O algoritmo apresentado, denominado Turquois, admite f < n 3 nós maliciosos e assegura progresso nos passos de comunicação em que dnf 2 e(n k f) + k 2. O algoritmo é sujeito a uma análise de desempenho comparativa com outros protocolos na literatura. Os resultados demonstram que, à medida que o número de nós no sistema aumenta, o desempenho do protocolo Turquois ultrapassa os restantes em mais do que uma ordem de magnitude.FC