508 research outputs found
Simple and Optimal Randomized Fault-Tolerant Rumor Spreading
We revisit the classic problem of spreading a piece of information in a group
of fully connected processors. By suitably adding a small dose of
randomness to the protocol of Gasienic and Pelc (1996), we derive for the first
time protocols that (i) use a linear number of messages, (ii) are correct even
when an arbitrary number of adversarially chosen processors does not
participate in the process, and (iii) with high probability have the
asymptotically optimal runtime of when at least an arbitrarily
small constant fraction of the processors are working. In addition, our
protocols do not require that the system is synchronized nor that all
processors are simultaneously woken up at time zero, they are fully based on
push-operations, and they do not need an a priori estimate on the number of
failed nodes.
Our protocols thus overcome the typical disadvantages of the two known
approaches, algorithms based on random gossip (typically needing a large number
of messages due to their unorganized nature) and algorithms based on fair
workload splitting (which are either not {time-efficient} or require intricate
preprocessing steps plus synchronization).Comment: This is the author-generated version of a paper which is to appear in
Distributed Computing, Springer, DOI: 10.1007/s00446-014-0238-z It is
available online from
http://link.springer.com/article/10.1007/s00446-014-0238-z This version
contains some new results (Section 6
Optimal Gossip with Direct Addressing
Gossip algorithms spread information by having nodes repeatedly forward
information to a few random contacts. By their very nature, gossip algorithms
tend to be distributed and fault tolerant. If done right, they can also be fast
and message-efficient. A common model for gossip communication is the random
phone call model, in which in each synchronous round each node can PUSH or PULL
information to or from a random other node. For example, Karp et al. [FOCS
2000] gave algorithms in this model that spread a message to all nodes in
rounds while sending only messages per node
on average.
Recently, Avin and Els\"asser [DISC 2013], studied the random phone call
model with the natural and commonly used assumption of direct addressing.
Direct addressing allows nodes to directly contact nodes whose ID (e.g., IP
address) was learned before. They show that in this setting, one can "break the
barrier" and achieve a gossip algorithm running in
rounds, albeit while using messages per node.
We study the same model and give a simple gossip algorithm which spreads a
message in only rounds. We also prove a matching lower bound which shows that this running time is best possible. In
particular we show that any gossip algorithm takes with high probability at
least rounds to terminate. Lastly, our algorithm can be
tweaked to send only messages per node on average with only
bits per message. Our algorithm therefore simultaneously achieves the optimal
round-, message-, and bit-complexity for this setting. As all prior gossip
algorithms, our algorithm is also robust against failures. In particular, if in
the beginning an oblivious adversary fails any nodes our algorithm still,
with high probability, informs all but surviving nodes
Bit-complexité des protocoles de gossip
National audienceNous étudions le problème du \emph{gossip} (i.e., diffusion de rumeurs) dans le modèle des appels aléatoires. Considérons noeuds communiquant en parallèle par étape. A chaque étape, un ensemble (potentiellement vide) de \emph{rumeurs} est généré à chaque noeud, la même rumeur pouvant être générée simultanément par plusieurs noeuds. L'objectif est de diffuser ces rumeurs à tous les noeuds. Pour ce faire, à chaque étape, chaque noeud appelle un autre noeud choisi uniformément aléatoirement parmi l'ensemble de tous les noeuds, et un noeud ne peut alors communiquer qu'avec le noeud qu'il a appelé, et les noeuds qui l'ont potentiellement appelé. Dans ce modèle, Karp et ses co-auteurs~\cite{Karp2000} ont montré qu'aucun algorithme de gossip ne peut être à la fois optimal en temps (i.e., s'exécuter en étapes) et en volume de communication (i.e., s'exécuter en transmettant au plus messages). En particulier, ils ont montré que tout algorithme de gossip n'utilisant pas les IDs des noeuds et diffusant toute rumeur en étapes doit échanger messages par rumeur. Karp et ses co-auteurs ont également montré que ce compromis peut être atteint. Dans cet article, nous étudions le volume de communication estimé en nombre de bits échangés plutôt qu'en nombre de messages. Nous montrons tout d'abord que tout algorithme de gossip n'utilisant pas les IDs des noeuds et diffusant toute rumeur en étapes doit échanger bits pour diffuser une rumeur de bits. Nous proposons alors un algorithme de gossip n'utilisant pas les IDs des noeuds qui diffuse toute rumeur en étapes, en échangeant bits pour une rumeur de bits. Ces résultats démontrent que contrairement à ce qu'il peut sembler lorsque l'on mesure le volume de communication en nombre de messages, il est possible d'être à la fois optimal en temps (i.e., s'exécuter en étapes) et en volume de communication (i.e., s'exécuter en transmettant au plus bits), sauf pour des rumeurs extrêmement petites, de taille bits
Gossip in a Smartphone Peer-to-Peer Network
In this paper, we study the fundamental problem of gossip in the mobile
telephone model: a recently introduced variation of the classical telephone
model modified to better describe the local peer-to-peer communication services
implemented in many popular smartphone operating systems. In more detail, the
mobile telephone model differs from the classical telephone model in three
ways: (1) each device can participate in at most one connection per round; (2)
the network topology can undergo a parameterized rate of change; and (3)
devices can advertise a parameterized number of bits about their state to their
neighbors in each round before connection attempts are initiated. We begin by
describing and analyzing new randomized gossip algorithms in this model under
the harsh assumption of a network topology that can change completely in every
round. We prove a significant time complexity gap between the case where nodes
can advertise bits to their neighbors in each round, and the case where
nodes can advertise bit. For the latter assumption, we present two
solutions: the first depends on a shared randomness source, while the second
eliminates this assumption using a pseudorandomness generator we prove to exist
with a novel generalization of a classical result from the study of two-party
communication complexity. We then turn our attention to the easier case where
the topology graph is stable, and describe and analyze a new gossip algorithm
that provides a substantial performance improvement for many parameters. We
conclude by studying a relaxed version of gossip in which it is only necessary
for nodes to each learn a specified fraction of the messages in the system.Comment: Extended Abstract to Appear in the Proceedings of the ACM Conference
on the Principles of Distributed Computing (PODC 2017
Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance
In this paper, we study the question of how efficiently a collection of
interconnected nodes can perform a global computation in the widely studied
GOSSIP model of communication. In this model, nodes do not know the global
topology of the network, and they may only initiate contact with a single
neighbor in each round. This model contrasts with the much less restrictive
LOCAL model, where a node may simultaneously communicate with all of its
neighbors in a single round. A basic question in this setting is how many
rounds of communication are required for the information dissemination problem,
in which each node has some piece of information and is required to collect all
others. In this paper, we give an algorithm that solves the information
dissemination problem in at most rounds in a network
of diameter , withno dependence on the conductance. This is at most an
additive polylogarithmic factor from the trivial lower bound of , which
applies even in the LOCAL model. In fact, we prove that something stronger is
true: any algorithm that requires rounds in the LOCAL model can be
simulated in rounds in the GOSSIP model. We thus
prove that these two models of distributed computation are essentially
equivalent
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
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