We study a well-known communication abstraction called Uniform Reliable Broadcast (URB). URB is central in the design and implementation of fault-tolerant distributed systems, as many non-trivial fault-tolerant distributed applications require communication with provable guarantees on message deliveries. Our study focuses on fault-tolerant implementations for time-free message-passing systems that are prone to node-failures. Moreover, we aim at the design of an even more robust communication abstraction. We do so through the lenses of self-stabilization---a very strong notion of fault-tolerance. In addition to node and communication failures, self-stabilizing algorithms can recover after the occurrence of arbitrary transient faults; these faults represent any violation of the assumptions according to which the system was designed to operate (as long as the algorithm code stays intact).
This work proposes the first self-stabilizing URB solution for time-free message-passing systems that are prone to node-failures. The proposed algorithm has an O(bufferUnitSize) stabilization time (in terms of asynchronous cycles) from arbitrary transient faults, where bufferUnitSize is a predefined constant that can be set according to the available memory. Moreover, the communication costs of our algorithm are similar to the ones of the non-self-stabilizing state-of-the-art. The main differences are that our proposal considers repeated gossiping of O(1) bits messages and deals with bounded space (which is a prerequisite for self-stabilization). Specifically, each node needs to store up to bufferUnitSize n records and each record is of size O(v + n log n) bits, where n is the number of nodes in the system and v is the number of bits needed to encode a single URB instance.
The problem of total-order (uniform reliable) broadcast is fundamental in fault-tolerant distributed computing since it abstracts a broad set of problems requiring processes to uniformly deliver messages in the same order in which they were sent. Existing solutions (that tolerate process failures) reduce the total-order broadcast problem to the one of multivalued consensus. Our study aims at the design of an even more reliable solution. We do so through the lenses of self-stabilization-a very strong notion of fault tolerance. In addition to node and communication failures, self-stabilizing alg…
We study a well-known communication abstraction called Byzantine Reliable Broadcast (BRB). This abstraction is central in the design and implementation of fault-tolerant distributed systems, as many fault-tolerant distributed applications require communication with provable guarantees on message deliveries. Our study focuses on fault-tolerant implementations for message-passing systems that are prone to process-failures, such as crashes and malicious behavior. At PODC 1983, Bracha and Toueg, in short, BT, solved the BRB problem. BT has optimal resilience since it can deal with t < n/3 Byzantin…
Memory Lower Bounds and Impossibility Results for Anonymous Dynamic Broadcast
School of Computing and Augmented Intelligence and Biodesign Center for Biocomputing, Security and Society Arizona State University（亚利桑那州立大学计算与增强智能学院及生物设计生物计算、安全与社会中心）
Development of many futuristic technologies, such as MANET, VANET, iThings, nano-devices, depend on efficient distributed communication protocols in multi-hop ad hoc networks. A vast majority of research in this area focus on design heuristic protocols, and analyze their performance by simulations on networks generated randomly or obtained in practical measurements of some (usually small-size) wireless networks. %some library. Moreover, they often assume access to truly random sources, which is often not reasonable in case of wireless devices. In this work we use a formal framework to study th…
Byzantine agreement algorithms typically assume implicit initial state consistency and synchronization among the correct nodes and then operate in coordinated rounds of information exchange to reach agreement based on the input values. The implicit initial assumptions enable correct nodes to infer about the progression of the algorithm at other nodes from their local state. This paper considers a more severe fault model than permanent Byzantine failures, one in which the system can in addition be subject to severe transient failures that can temporarily throw the system out of its assumption b…
We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing protocols. The first stage is a uniform randomized stabilizing {\em unique naming} protocol, and the second stage is a stabilizing {\em MDST} protocol, designed as a {\em fair composition} of Merlin--Segall's stabilizing protocol and a distributed deterministic stabilizing protocol solving the (MDST) problem. The resulting randomized distributed algorithm presented…
In the advent of large-scale multi-hop wireless technologies, such as MANET, VANET, iThings, it is of utmost importance to devise efficient distributed protocols to maintain network architecture and provide basic communication tools. One of such fundamental communication tasks is broadcast, also known as a 1-to-all communication. We propose several new efficient distributed algorithms and evaluate their time performance both theoretically and by simulations. First randomized algorithm accomplishes broadcast in O(D+log(1/d)) rounds with probability at least 1-d on any uniform-power network of n…
Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the pr…
The Reliable Broadcast concept allows an honest party to send a message to all other parties and to make sure that all honest parties receive this message. In addition, it allows an honest party that received a message to know that all other honest parties would also receive the same message. This technique is important to ensure distributed consistency when facing failures. In the current paper, we study the ability to use \RR to consistently transmit a sequence of input values in an asynchronous environment with a designated sender. The task can be easily achieved using counters, but cannot …
The majority of the literature on consensus assumes that protocols are jointly started at all nodes of the distributed system. We show how to remove this problematic assumption in semi-synchronous systems, where messages delays and relative drifts of local clocks may vary arbitrarily within known bounds. Our framework is self-stabilizing and efficient both in terms of communication and time; more concretely, compared to a synchronous start in a synchronous model of a non-self-stabilizing protocol, we achieve a constant-factor increase in the time and communicated bits to complete an instance, …
This paper considers the basic $\mathcal{PULL}$ model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of $n$ agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let …
We study the following synchronous process that we call "repeated balls-into-bins". The process is started by assigning $n$ balls to $n$ bins in an arbitrary way. In every subsequent round, from each non-empty bin one ball is chosen according to some fixed strategy (random, FIFO, etc), and re-assigned to one of the $n$ bins uniformly at random. We define a configuration "legitimate" if its maximum load is $\mathcal{O}(\log n)$. We prove that, starting from any configuration, the process will converge to a legitimate configuration in linear time and then it will only take on legitimate configur…
The problem of multivalued consensus is fundamental in the area of fault-tolerant distributed computing since it abstracts a very broad set of agreement problems in which processes have to uniformly decide on a specific value v in V, where |V| >1. Existing solutions (that tolerate process failures) reduce the multivalued consensus problem to the one of binary consensus, e.g., Mostefaoui-Raynal-Tronel and Zhang-Chen. Our study aims at the design of an even more reliable solution. We do so through the lenses of self-stabilization -- a very strong notion of fault-tolerance. In addition to node an…
Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, $ξ$, and then combine them into frames of uniform size, $τ$. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, $δ$, and no access to external references for collision detection, time or position, we consider the problem of collision-free self-stabilizing TDMA algorithms that use constant frame size. We demonstrate that this problem has no …
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^…
A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the system recovers from this catastrophic situation without external intervention in finite time. In this paper, we consider the problem of constructing self-stabilizingly a \emph{maximal independent set} in uniform unidirectional networks of arbitrary shape. On the negative side, we present evidence that in uniform networks, \emph{deterministic} self-stabilization of this problem is \emph{impossible}. Also, the \emph{silence} property (\emph{i.e.} having communi…
We give efficient algorithms for the fundamental problems of Broadcast and Local Broadcast in dynamic wireless networks. We propose a general model of communication which captures and includes both fading models (like SINR) and graph-based models (such as quasi unit disc graphs, bounded-independence graphs, and protocol model). The only requirement is that the nodes can be embedded in a bounded growth quasi-metric, which is the weakest condition known to ensure distributed operability. Both the nodes and the links of the network are dynamic: nodes can come and go, while the signal strength on …
In this paper we present the self-stabilizing implementation of a class of token based algorithms. In the current work we only consider interactions between weak nodes. They are uniform, they do not have unique identifiers, are static and their interactions are restricted to a subset of nodes called neighbours. While interacting, a pair of neighbouring nodes may create mobile agents (that materialize in the current work the token abstraction) that perform traversals of the network and accelerate the system stabilization. In this work we only explore the power of oblivious stateless agents. Our…
We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $Σ$. The system must converge toward a consensus state in which all, or almost all nodes, hold the same opinion. Moreover, this opinion should be \emph{valid}, i.e., it should be one among those initially present in the system. This condition should be met even in the presence of an adaptive, malicious adversary who can modify the opinions of a bounded number of nodes in every round. We consider the \…
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modeled as static balls into bins processes, where $m$ balls (tasks) are to be distributed to $n$ bins (servers). In a seminal work, Azar et al. proposed the sequential strategy \greedy{d} for $n=m$. When thrown, a ball queries the load of $d$ random bins and is allocated to a least loaded of these. Azar et al. showed that $d=2$ yields an exponential improvement compared to $d=1$. Berenbrink et al. extended this to $m\gg n$,…
We consider the multihop broadcasting problem for $n$ nodes placed uniformly at random in a disk and investigate the number of hops required to transmit a signal from the central node to all other nodes under three communication models: Unit-Disk-Graph (UDG), Signal-to-Noise-Ratio (SNR), and the wave superposition model of multiple input/multiple output (MIMO). In the MIMO model, informed nodes cooperate to produce a stronger superposed signal. We do not consider the problem of transmitting a full message nor do we consider interference. In each round, the informed senders try to deliver to ot…
Clustering is a promising approach for building hierarchies and simplifying the routing process in mobile ad-hoc network environments. The main objective of clustering is to identify suitable node representatives, i.e. cluster heads (CHs), to store routing and topology information and maximize clusters stability. Traditional clustering algorithms suggest CH election exclusively based on node IDs or location information and involve frequent broadcasting of control packets, even when network topology remains unchanged. More recent works take into account additional metrics (such as energy and mo…
We present Cobalt, a novel atomic broadcast algorithm that works in networks with non-uniform trust and no global agreement on participants, and is probabilistically guaranteed to make forward progress even in the presence of maximal faults and arbitrary asynchrony. The exact properties that Cobalt satisfies makes it particularly applicable to designing an efficient decentralized "voting network" that allows a public, open-entry group of nodes to agree on changes to some shared set of rules in a fair and consistent manner while tolerating some trusted nodes and arbitrarily many untrusted nodes…
Gossip and in particular network coded algebraic gossip have recently attracted attention as a fast, bandwidth-efficient, reliable and distributed way to broadcast or multicast multiple messages. While the algorithms are simple, involved queuing approaches are used to study their performance. The most recent result in this direction shows that uniform algebraic gossip disseminates k messages in O(Δ(D + k + log n)) rounds where D is the diameter, n the size of the network and Δ the maximum degree. In this paper we give a simpler, short and self-contained proof for this worst-case guarantee. Our…
