5,248 research outputs found
Collaborative Broadcast in O(log log n) Rounds
We consider the multihop broadcasting problem for nodes placed uniformly
at random in a disk and investigate the number of hops required to transmit a
signal from the central node to all other nodes under three communication
models: Unit-Disk-Graph (UDG), Signal-to-Noise-Ratio (SNR), and the wave
superposition model of multiple input/multiple output (MIMO). In the MIMO
model, informed nodes cooperate to produce a stronger superposed signal. We do
not consider the problem of transmitting a full message nor do we consider
interference. In each round, the informed senders try to deliver to other nodes
the required signal strength such that the received signal can be distinguished
from the noise. We assume sufficiently high node density . In the unit-disk graph model, broadcasting needs
rounds. In the other models, we use an Expanding Disk Broadcasting Algorithm,
where in a round only triggered nodes within a certain distance from the
initiator node contribute to the broadcasting operation. This algorithm
achieves a broadcast in only rounds in the
SNR-model. Adapted to the MIMO model, it broadcasts within rounds. All bounds are asymptotically tight and hold with high
probability, i.e. .Comment: extended abstract accepted for ALGOSENSORS 201
Distributed Exploration in Multi-Armed Bandits
We study exploration in Multi-Armed Bandits in a setting where players
collaborate in order to identify an -optimal arm. Our motivation
comes from recent employment of bandit algorithms in computationally intensive,
large-scale applications. Our results demonstrate a non-trivial tradeoff
between the number of arm pulls required by each of the players, and the amount
of communication between them. In particular, our main result shows that by
allowing the players to communicate only once, they are able to learn
times faster than a single player. That is, distributing learning to
players gives rise to a factor parallel speed-up. We complement
this result with a lower bound showing this is in general the best possible. On
the other extreme, we present an algorithm that achieves the ideal factor
speed-up in learning performance, with communication only logarithmic in
Decentralized Exploration in Multi-Armed Bandits
We consider the decentralized exploration problem: a set of players
collaborate to identify the best arm by asynchronously interacting with the
same stochastic environment. The objective is to insure privacy in the best arm
identification problem between asynchronous, collaborative, and thrifty
players. In the context of a digital service, we advocate that this
decentralized approach allows a good balance between the interests of users and
those of service providers: the providers optimize their services, while
protecting the privacy of the users and saving resources. We define the privacy
level as the amount of information an adversary could infer by intercepting the
messages concerning a single user. We provide a generic algorithm Decentralized
Elimination, which uses any best arm identification algorithm as a subroutine.
We prove that this algorithm insures privacy, with a low communication cost,
and that in comparison to the lower bound of the best arm identification
problem, its sample complexity suffers from a penalty depending on the inverse
of the probability of the most frequent players. Then, thanks to the genericity
of the approach, we extend the proposed algorithm to the non-stationary
bandits. Finally, experiments illustrate and complete the analysis
Computation-Aware Data Aggregation
Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes\u27 input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do not take compute time into account. Rather, most distributed models of computation only explicitly consider communication time.
In this paper, we introduce a model of distributed computation that considers both computation and communication so as to give a theoretical treatment of data aggregation. We study both the structure of and how to compute the fastest data aggregation schedule in this model. As our first result, we give a polynomial-time algorithm that computes the optimal schedule when the input network is a complete graph. Moreover, since one may want to aggregate data over a pre-existing network, we also study data aggregation scheduling on arbitrary graphs. We demonstrate that this problem on arbitrary graphs is hard to approximate within a multiplicative 1.5 factor. Finally, we give an O(log n ? log(OPT/t_m))-approximation algorithm for this problem on arbitrary graphs, where n is the number of nodes and OPT is the length of the optimal schedule
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