19 research outputs found
Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks
We show that randomization can lead to significant improvements for a few
fundamental problems in distributed tracking. Our basis is the {\em
count-tracking} problem, where there are players, each holding a counter
that gets incremented over time, and the goal is to track an
\eps-approximation of their sum continuously at all times,
using minimum communication. While the deterministic communication complexity
of the problem is \Theta(k/\eps \cdot \log N), where is the final value
of when the tracking finishes, we show that with randomization, the
communication cost can be reduced to \Theta(\sqrt{k}/\eps \cdot \log N). Our
algorithm is simple and uses only O(1) space at each player, while the lower
bound holds even assuming each player has infinite computing power. Then, we
extend our techniques to two related distributed tracking problems: {\em
frequency-tracking} and {\em rank-tracking}, and obtain similar improvements
over previous deterministic algorithms. Both problems are of central importance
in large data monitoring and analysis, and have been extensively studied in the
literature.Comment: 19 pages, 1 figur
Communication-Efficient Weighted Reservoir Sampling from Fully Distributed Data Streams
We consider weighted random sampling from distributed data streams presented as a sequence of mini-batches of items. This is a natural model for distributed streaming computation, and our goal is to showcase its usefulness. We present and analyze a fully distributed, communication-efficient algorithm for weighted reservoir sampling in this model. An experimental evaluation on up to 256 nodes (5120 processors) shows good speedups, while theoretical analysis promises further scaling to much larger machines
Weighted Reservoir Sampling from Distributed Streams
We consider message-efficient continuous random sampling from a distributed
stream, where the probability of inclusion of an item in the sample is
proportional to a weight associated with the item. The unweighted version,
where all weights are equal, is well studied, and admits tight upper and lower
bounds on message complexity. For weighted sampling with replacement, there is
a simple reduction to unweighted sampling with replacement. However, in many
applications the stream has only a few heavy items which may dominate a random
sample when chosen with replacement. Weighted sampling \textit{without
replacement} (weighted SWOR) eludes this issue, since such heavy items can be
sampled at most once.
In this work, we present the first message-optimal algorithm for weighted
SWOR from a distributed stream. Our algorithm also has optimal space and time
complexity. As an application of our algorithm for weighted SWOR, we derive the
first distributed streaming algorithms for tracking \textit{heavy hitters with
residual error}. Here the goal is to identify stream items that contribute
significantly to the residual stream, once the heaviest items are removed.
Residual heavy hitters generalize the notion of heavy hitters and are
important in streams that have a skewed distribution of weights. In addition to
the upper bound, we also provide a lower bound on the message complexity that
is nearly tight up to a factor. Finally, we use our weighted
sampling algorithm to improve the message complexity of distributed
tracking, also known as count tracking, which is a widely studied problem in
distributed streaming. We also derive a tight message lower bound, which closes
the message complexity of this fundamental problem.Comment: To appear in PODS 201
Communication-Efficient (Weighted) Reservoir Sampling from Fully Distributed Data Streams
We consider communication-efficient weighted and unweighted (uniform) random
sampling from distributed data streams presented as a sequence of mini-batches
of items. This is a natural model for distributed streaming computation, and
our goal is to showcase its usefulness. We present and analyze fully
distributed, communication-efficient algorithms for both versions of the
problem. An experimental evaluation of weighted reservoir sampling on up to 256
nodes (5120 processors) shows good speedups, while theoretical analysis
promises further scaling to much larger machines.Comment: A previous version of this paper was titled "Communication-Efficient
(Weighted) Reservoir Sampling
Distinct random sampling from a distributed stream
We consider continuous maintenance of a random sample of distinct elements from a massive data stream, whose input elements are observed at multiple distributed sites that communicate via a central coordinator. At any point, when a query is received at the coordinator, it responds with a random sample from the set of all distinct elements observed at the different sites so far. We present the first algorithms for distinct random sampling on distributed streams. We also present a lower bound on the expected number of messages that must be transmitted by any distributed algorithm, showing that our algorithm is message optimal to within a factor of four. We present extensions to sliding windows, and detailed experimental results showing the performance of our algorithm on real-world data sets
Frequency Estimation Under Multiparty Differential Privacy: One-shot and Streaming
We study the fundamental problem of frequency estimation under both privacy
and communication constraints, where the data is distributed among parties.
We consider two application scenarios: (1) one-shot, where the data is static
and the aggregator conducts a one-time computation; and (2) streaming, where
each party receives a stream of items over time and the aggregator continuously
monitors the frequencies. We adopt the model of multiparty differential privacy
(MDP), which is more general than local differential privacy (LDP) and
(centralized) differential privacy. Our protocols achieve optimality (up to
logarithmic factors) permissible by the more stringent of the two constraints.
In particular, when specialized to the -LDP model, our protocol
achieves an error of using bits of communication and
bits of public randomness, where is the size of the domain