3,845 research outputs found
Faster rumor spreading with multiple calls
We consider the random phone call model introduced by Demers et al., which is a well-studied model for information dissemination in networks. One basic protocol in this model is the so-called Push protocol that proceeds in synchronous rounds. Starting with a single node which knows of a rumor, every informed node calls in each round a random neighbor and informs it of the rumor. The Push-Pull protocol works similarly, but additionally every uninformed node calls a random neighbor and may learn the rumor from it. It is well-known that both protocols need Θ(log n) rounds to spread a rumor on a complete network with n nodes. Here we are interested in how much the spread can be speeded up by enabling nodes to make more than one call in each round. We propose a new model where the number of calls of a node is chosen independently according to a probability distribution R. We provide both lower and upper bounds on the rumor spreading time depending on statistical properties of R such as the mean or the variance (if they exist). In particular, if R follows a power law distribution with exponent β ∈ (2, 3), we show that the Push-Pull protocol spreads a rumor in Θ(log log n) rounds. Moreover, when β = 3, the Push- Pull protocol spreads a rumor in Θ(formula presented) rounds
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
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
Strong Robustness of Randomized Rumor Spreading Protocols
Randomized rumor spreading is a classical protocol to disseminate information
across a network. At SODA 2008, a quasirandom version of this protocol was
proposed and competitive bounds for its run-time were proven. This prompts the
question: to what extent does the quasirandom protocol inherit the second
principal advantage of randomized rumor spreading, namely robustness against
transmission failures?
In this paper, we present a result precise up to factors. We
limit ourselves to the network in which every two vertices are connected by a
direct link. Run-times accurate to their leading constants are unknown for all
other non-trivial networks.
We show that if each transmission reaches its destination with a probability
of , after (1+\e)(\frac{1}{\log_2(1+p)}\log_2n+\frac{1}{p}\ln n)
rounds the quasirandom protocol has informed all nodes in the network with
probability at least 1-n^{-p\e/40}. Note that this is faster than the
intuitively natural factor increase over the run-time of approximately
for the non-corrupted case.
We also provide a corresponding lower bound for the classical model. This
demonstrates that the quasirandom model is at least as robust as the fully
random model despite the greatly reduced degree of independent randomness.Comment: Accepted for publication in "Discrete Applied Mathematics". A short
version appeared in the proceedings of the 20th International Symposium on
Algorithms and Computation (ISAAC 2009). Minor typos fixed in the second
version. Proofs of Lemma 11 and Theorem 12 fixed in the third version. Proof
of Lemma 8 fixed in the fourth versio
Information spreading during emergencies and anomalous events
The most critical time for information to spread is in the aftermath of a
serious emergency, crisis, or disaster. Individuals affected by such situations
can now turn to an array of communication channels, from mobile phone calls and
text messages to social media posts, when alerting social ties. These channels
drastically improve the speed of information in a time-sensitive event, and
provide extant records of human dynamics during and afterward the event.
Retrospective analysis of such anomalous events provides researchers with a
class of "found experiments" that may be used to better understand social
spreading. In this chapter, we study information spreading due to a number of
emergency events, including the Boston Marathon Bombing and a plane crash at a
western European airport. We also contrast the different information which may
be gleaned by social media data compared with mobile phone data and we estimate
the rate of anomalous events in a mobile phone dataset using a proposed anomaly
detection method.Comment: 19 pages, 11 figure
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