264 research outputs found
Breaking the log n barrier on rumor spreading
rounds has been a well known upper bound for rumor spreading
using push&pull in the random phone call model (i.e., uniform gossip in the
complete graph). A matching lower bound of is also known for
this special case. Under the assumption of this model and with a natural
addition that nodes can call a partner once they learn its address (e.g., its
IP address) we present a new distributed, address-oblivious and robust
algorithm that uses push&pull with pointer jumping to spread a rumor to all
nodes in only rounds, w.h.p. This algorithm can also cope
with node failures, in which case all but
nodes become informed within rounds, w.h.p
Robustness of Randomized Rumour Spreading
In this work we consider three well-studied broadcast protocols: Push, Pull
and Push&Pull. A key property of all these models, which is also an important
reason for their popularity, is that they are presumed to be very robust, since
they are simple, randomized, and, crucially, do not utilize explicitly the
global structure of the underlying graph. While sporadic results exist, there
has been no systematic theoretical treatment quantifying the robustness of
these models. Here we investigate this question with respect to two orthogonal
aspects: (adversarial) modifications of the underlying graph and message
transmission failures.
We explore in particular the following notion of Local Resilience: beginning
with a graph, we investigate up to which fraction of the edges an adversary has
to be allowed to delete at each vertex, so that the protocols need
significantly more rounds to broadcast the information. Our main findings
establish a separation among the three models. It turns out that Pull is robust
with respect to all parameters that we consider. On the other hand, Push may
slow down significantly, even if the adversary is allowed to modify the degrees
of the vertices by an arbitrarily small positive fraction only. Finally,
Push&Pull is robust when no message transmission failures are considered,
otherwise it may be slowed down.
On the technical side, we develop two novel methods for the analysis of
randomized rumour spreading protocols. First, we exploit the notion of
self-bounding functions to facilitate significantly the round-based analysis:
we show that for any graph the variance of the growth of informed vertices is
bounded by its expectation, so that concentration results follow immediately.
Second, in order to control adversarial modifications of the graph we make use
of a powerful tool from extremal graph theory, namely Szemer\`edi's Regularity
Lemma.Comment: version 2: more thorough literature revie
Asynchronous Rumour Spreading in Social and Signed Topologies
In this paper, we present an experimental analysis of the asynchronous push &
pull rumour spreading protocol. This protocol is, to date, the best-performing
rumour spreading protocol for simple, scalable, and robust information
dissemination in distributed systems. We analyse the effect that multiple
parameters have on the protocol's performance, such as using memory to avoid
contacting the same neighbor twice in a row, varying the stopping criteria used
by nodes to decide when to stop spreading the rumour, employing more
sophisticated neighbor selection policies instead of the standard uniform
random choice, and others. Prior work has focused on either providing
theoretical upper bounds regarding the number of rounds needed to spread the
rumour to all nodes, or, proposes improvements by adjusting isolated
parameters. To our knowledge, our work is the first to study how multiple
parameters affect system behaviour both in isolation and combination and under
a wide range of values. Our analysis is based on experimental simulations using
real-world social network datasets, thus complementing prior theoretical work
to shed light on how the protocol behaves in practical, real-world systems. We
also study the behaviour of the protocol on a special type of social graph,
called signed networks (e.g., Slashdot and Epinions), whose links indicate
stronger trust relationships. Finally, through our detailed analysis, we
demonstrate how a few simple additions to the protocol can improve the total
time required to inform 100% of the nodes by a maximum of 99.69% and an average
of 82.37%.Comment: 10 pages, 4 figures, 5 table
Forwarding Without Repeating: Efficient Rumor Spreading in Bounded-Degree Graphs
We study a gossip protocol called forwarding without repeating (FWR). The
objective is to spread multiple rumors over a graph as efficiently as possible.
FWR accomplishes this by having nodes record which messages they have forwarded
to each neighbor, so that each message is forwarded at most once to each
neighbor. We prove that FWR spreads a rumor over a strongly connected digraph,
with high probability, in time which is within a constant factor of optimal for
digraphs with bounded out-degree. Moreover, on digraphs with bounded out-degree
and bounded number of rumors, the number of transmissions required by FWR is
arbitrarily better than that of existing approaches. Specifically, FWR requires
O(n) messages on bounded-degree graphs with n nodes, whereas classical
forwarding and an approach based on network coding both require {\omega}(n)
messages. Our results are obtained using combinatorial and probabilistic
arguments. Notably, they do not depend on expansion properties of the
underlying graph, and consequently the message complexity of FWR is arbitrarily
better than classical forwarding even on constant-degree expander graphs, as n
\rightarrow \infty. In resource-constrained applications, where each
transmission consumes battery power and bandwidth, our results suggest that
using a small amount of memory at each node leads to a significant savings.Comment: 16 page
Discovery through Gossip
We study randomized gossip-based processes in dynamic networks that are
motivated by discovery processes in large-scale distributed networks like
peer-to-peer or social networks.
A well-studied problem in peer-to-peer networks is the resource discovery
problem. There, the goal for nodes (hosts with IP addresses) is to discover the
IP addresses of all other hosts. In social networks, nodes (people) discover
new nodes through exchanging contacts with their neighbors (friends). In both
cases the discovery of new nodes changes the underlying network - new edges are
added to the network - and the process continues in the changed network.
Rigorously analyzing such dynamic (stochastic) processes with a continuously
self-changing topology remains a challenging problem with obvious applications.
This paper studies and analyzes two natural gossip-based discovery processes.
In the push process, each node repeatedly chooses two random neighbors and puts
them in contact (i.e., "pushes" their mutual information to each other). In the
pull discovery process, each node repeatedly requests or "pulls" a random
contact from a random neighbor. Both processes are lightweight, local, and
naturally robust due to their randomization.
Our main result is an almost-tight analysis of the time taken for these two
randomized processes to converge. We show that in any undirected n-node graph
both processes take O(n log^2 n) rounds to connect every node to all other
nodes with high probability, whereas Omega(n log n) is a lower bound. In the
directed case we give an O(n^2 log n) upper bound and an Omega(n^2) lower bound
for strongly connected directed graphs. A key technical challenge that we
overcome is the analysis of a randomized process that itself results in a
constantly changing network which leads to complicated dependencies in every
round.Comment: 19 page
Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise
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 protocol. Using this reduction, we get, among other
applications, the first logarithmic lower bound on the number of rounds needed
to achieve Consensus in the uniform GOSSIP model on the complete graph. The
lower bound is tight and, in this model, Consensus and Broadcast are
equivalent.
We then turn to distributed models with noisy communication channels that
have been studied in the context of some bio-inspired systems. In such models,
only one noisy bit is exchanged when a communication channel is established
between two nodes, and so one cannot easily simulate a noiseless protocol by
using error-correcting codes. An lower bound on the
number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS
Comp. Bio. 2018] in one such model (noisy uniform PULL, where is a
parameter that measures the amount of noise). In such model, we prove a new
bound for Broadcast and a
bound for binary Consensus, thus establishing an
exponential gap between the number of rounds necessary for Consensus versus
Broadcast
Algorithm for Achieving Consensus Over Conflicting Rumors: Convergence Analysis and Applications
Motivated by the large expansion in the study of social networks, this paper
deals with the problem of multiple messages spreading over the same network
using gossip algorithms. Given two messages distributed over some nodes of the
graph, we first investigate the final distribution of the messages given an
initial state. Then, an algorithm is presented to achieve consensus over one of
the messages. Finally, a game theoretical application and an analogy with
word-of-mouth marketing are outlined.Comment: IEEE Student Paper Contes
Randomized Rumor Spreading in Ad Hoc Networks with Buffers
The randomized rumor spreading problem generates a big interest in the area
of distributed algorithms due to its simplicity, robustness and wide range of
applications. The two most popular communication paradigms used for spreading
the rumor are Push and Pull algorithms. The former protocol allows nodes to
send the rumor to a randomly selected neighbor at each step, while the latter
is based on sending a request and downloading the rumor from a randomly
selected neighbor, provided the neighbor has it. Previous analysis of these
protocols assumed that every node could process all such push/pull operations
within a single step, which could be unrealistic in practical situations.
Therefore we propose a new framework for analysis rumor spreading accommodating
buffers, in which a node can process only one push/pull message or push request
at a time. We develop upper and lower bounds for randomized rumor spreading
time in the new framework, and compare the results with analogous in the old
framework without buffers.Comment: Manuscript submitted to DISC 201
Tight bounds for rumor spreading in graphs of a given conductance
We study the connection between the rate at which a rumor spreads throughout a graph and the conductance of the graph -- a standard measure of a graph\u27s expansion properties.
We show that for any n-node graph with conductance phi, the classical PUSH-PULL algorithm distributes a rumor to all nodes of the graph in O(phi^(-1) log(n)) rounds with high probability (w.h.p.). This bound improves a recent result of Chierichetti, Lattanzi, and Panconesi [STOC 2010], and it is tight in the sense that there exist graphs where Omega(phi^(-1)log(n)) rounds of the PUSH-PULL algorithm are required to distribute a rumor w.h.p.
We also explore the PUSH and the PULL algorithms, and derive conditions that are both necessary and sufficient for the above upper bound to hold for those algorithms as well.
An interesting finding is that every graph contains a node such that the PULL algorithm takes O(phi^(-1) log(n)) rounds w.h.p. to distribute a rumor started at that node.
In contrast, there are graphs where the PUSH algorithm requires significantly more rounds for any start node
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