197 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
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
Distributed House-Hunting in Ant Colonies
We introduce the study of the ant colony house-hunting problem from a
distributed computing perspective. When an ant colony's nest becomes unsuitable
due to size constraints or damage, the colony must relocate to a new nest. The
task of identifying and evaluating the quality of potential new nests is
distributed among all ants. The ants must additionally reach consensus on a
final nest choice and the full colony must be transported to this single new
nest. Our goal is to use tools and techniques from distributed computing theory
in order to gain insight into the house-hunting process.
We develop a formal model for the house-hunting problem inspired by the
behavior of the Temnothorax genus of ants. We then show a \Omega(log n) lower
bound on the time for all n ants to agree on one of k candidate nests. We also
present two algorithms that solve the house-hunting problem in our model. The
first algorithm solves the problem in optimal O(log n) time but exhibits some
features not characteristic of natural ant behavior. The second algorithm runs
in O(k log n) time and uses an extremely simple and natural rule for each ant
to decide on the new nest.Comment: To appear in PODC 201
Spread of Information and Diseases via Random Walks in Sparse Graphs
We consider a natural network diffusion process, modeling the spread of information or infectious diseases. Multiple mobile agents perform independent simple random walks on an n-vertex connected graph G. The number of agents is linear in n and the walks start from the stationary distribution. Initially, a single vertex has a piece of information (or a virus). An agent becomes informed (or infected) the first time it visits some vertex with the information (or virus); thereafter, the agent informs (infects) all vertices it visits. Giakkoupis et al. (PODC'19) have shown that the spreading time, i.e., the time before all vertices are informed, is asymptotically and w.h.p. the same as in the well-studied randomized rumor spreading process, on any d-regular graph with d=Ω(logn). The case of sub-logarithmic degree was left open, and is the main focus of this paper. First, we observe that the equivalence shown by Giakkoupis et al. does not hold for small d: We give an example of a 3-regular graph with logarithmic diameter for which the expected spreading time is Ω(log^2n/loglogn), whereas randomized rumor spreading is completed in time Î(logn), w.h.p. Next, we show a general upper bound of O~(dâ
diam(G)+log^3n/d), w.h.p., for the spreading time on any d-regular graph. We also provide a version of the bound based on the average degree, for non-regular graphs. Next, we give tight analyses for specific graph families. We show that the spreading time is O(logn), w.h.p., for constant-degree regular expanders. For the binary tree, we show an upper bound of O(lognâ
loglogn), w.h.p., and prove that this is tight, by giving a matching lower bound for the cover time of the tree by n random walks. Finally, we show a bound of O(diam(G)), w.h.p., for k-dimensional grids, by adapting a technique by Kesten and Sidoravicius.Supported in part by ANR Project PAMELA (ANR16-CE23-0016-01).
Gates Cambridge Scholarship programme.
Supported by the ERC Grant `Dynamic Marchâ
Message and time efficient multi-broadcast schemes
We consider message and time efficient broadcasting and multi-broadcasting in
wireless ad-hoc networks, where a subset of nodes, each with a unique rumor,
wish to broadcast their rumors to all destinations while minimizing the total
number of transmissions and total time until all rumors arrive to their
destination. Under centralized settings, we introduce a novel approximation
algorithm that provides almost optimal results with respect to the number of
transmissions and total time, separately. Later on, we show how to efficiently
implement this algorithm under distributed settings, where the nodes have only
local information about their surroundings. In addition, we show multiple
approximation techniques based on the network collision detection capabilities
and explain how to calibrate the algorithms' parameters to produce optimal
results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459
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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