6 research outputs found
Efficient Counting with Optimal Resilience
In the synchronous -counting problem, we are given a synchronous system of nodes, where up to of the nodes may be Byzantine, that is, have arbitrary faulty behaviour. The task is to have all of the correct nodes count modulo in unison in a self-stabilising manner: regardless of the initial state of the system and the faulty nodes' behavior, eventually rounds are consistently labelled by a counter modulo at all correct nodes. We provide a deterministic solution with resilience that stabilises in rounds and every correct node broadcasts bits per round. We build and improve on a recent result offering stabilisation time and communication complexity but with sub-optimal resilience (PODC 2015). Our new algorithm has optimal resilience, asymptotically optimal stabilisation time, and low communication complexity. Finally, we modify the algorithm to guarantee that after stabilisation very little communication occurs. In particular, for optimal resilience and polynomial counter size , the algorithm broadcasts only bits per node every rounds without affecting the other properties of the algorithm; communication-wise this is asymptotically optimal
EFFICIENT COUNTING WITH OPTIMAL RESILIENCE
Consider a complete communication network of n nodes, where the nodes receive a common clock pulse. We study the synchronous c-counting problem: given any starting state and up to f faulty nodes with arbitrary behavior, the task is to eventually have all correct nodes labeling the pulses with increasing values modulo c in agreement. Thus, we are considering algorithms that are self-stabilizing despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have optimal resilience, (3) have a linear stabilization time in f (asymptotically optimal), (4) use a small number of states, and, consequently, (5) communicate a small number of bits per round. Prior algorithms either resort to randomization, use a large number of states and need high communication bandwidth, or have suboptimal resilience. In particular, we achieve an exponential improvement in both state complexity and message size for deterministic algorithms. Moreover, we present two complementary approaches for reducing the number of bits communicated during and after stabilization.Peer reviewe
Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits
This paper considers the basic 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 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 all agents converge
their output bits on the most frequent input bit of the sources (the majority
bit). Note that the particular case of a single source agent corresponds to the
classical problem of Broadcast. We concentrate on the severe fault-tolerant
context of self-stabilization, in which a correct configuration must be reached
eventually, despite all agents starting the execution with arbitrary initial
states.
We first design a general compiler which can essentially transform any
self-stabilizing algorithm with a certain property that uses -bits
messages to one that uses only -bits messages, while paying only a
small penalty in the running time. By applying this compiler recursively we
then obtain a self-stabilizing Clock Synchronization protocol, in which agents
synchronize their clocks modulo some given integer , within rounds w.h.p., and using messages that contain bits only.
We then employ the new Clock Synchronization tool to obtain a
self-stabilizing Majority Bit Dissemination protocol which converges in time, w.h.p., on every initial configuration, provided that the
ratio of sources supporting the minority opinion is bounded away from half.
Moreover, this protocol also uses only 3 bits per interaction.Comment: 28 pages, 4 figure
Efficient Counting with Optimal Resilience
In the synchronous -counting problem, we are given a synchronous system of nodes, where up to of the nodes may be Byzantine, that is, have arbitrary faulty behaviour. The task is to have all of the correct nodes count modulo in unison in a self-stabilising manner: regardless of the initial state of the system and the faulty nodes' behavior, eventually rounds are consistently labelled by a counter modulo at all correct nodes. We provide a deterministic solution with resilience that stabilises in rounds and every correct node broadcasts bits per round. We build and improve on a recent result offering stabilisation time and communication complexity but with sub-optimal resilience (PODC 2015). Our new algorithm has optimal resilience, asymptotically optimal stabilisation time, and low communication complexity. Finally, we modify the algorithm to guarantee that after stabilisation very little communication occurs. In particular, for optimal resilience and polynomial counter size , the algorithm broadcasts only bits per node every rounds without affecting the other properties of the algorithm; communication-wise this is asymptotically optimal