25 research outputs found
Optimal Elephant Flow Detection
Monitoring the traffic volumes of elephant flows, including the total byte
count per flow, is a fundamental capability for online network measurements. We
present an asymptotically optimal algorithm for solving this problem in terms
of both space and time complexity. This improves on previous approaches, which
can only count the number of packets in constant time. We evaluate our work on
real packet traces, demonstrating an up to X2.5 speedup compared to the best
alternative.Comment: Accepted to IEEE INFOCOM 201
Efficient Summing over Sliding Windows
This paper considers the problem of maintaining statistic aggregates over the
last W elements of a data stream. First, the problem of counting the number of
1's in the last W bits of a binary stream is considered. A lower bound of
{\Omega}(1/{\epsilon} + log W) memory bits for W{\epsilon}-additive
approximations is derived. This is followed by an algorithm whose memory
consumption is O(1/{\epsilon} + log W) bits, indicating that the algorithm is
optimal and that the bound is tight. Next, the more general problem of
maintaining a sum of the last W integers, each in the range of {0,1,...,R}, is
addressed. The paper shows that approximating the sum within an additive error
of RW{\epsilon} can also be done using {\Theta}(1/{\epsilon} + log W) bits for
{\epsilon}={\Omega}(1/W). For {\epsilon}=o(1/W), we present a succinct
algorithm which uses B(1 + o(1)) bits, where B={\Theta}(Wlog(1/W{\epsilon})) is
the derived lower bound. We show that all lower bounds generalize to randomized
algorithms as well. All algorithms process new elements and answer queries in
O(1) worst-case time.Comment: A shorter version appears in SWAT 201
On the Power of False Negative Awareness in Indicator-based Caching Systems
Distributed caching systems such as content distribution networks often
advertise their content via lightweight approximate indicators (e.g., Bloom
filters) to efficiently inform clients where each datum is likely cached. While
false-positive indications are necessary and well understood, most existing
works assume no false-negative indications. Our work illustrates practical
scenarios where false-negatives are unavoidable and ignoring them has a
significant impact on system performance. Specifically, we focus on
false-negatives induced by indicator staleness, which arises whenever the
system advertises the indicator only periodically, rather than immediately
reporting every change in the cache. Such scenarios naturally occur, e.g., in
bandwidth-constraint environments or when latency impedes the ability of each
client to obtain an updated indicator. Our work introduces novel false-negative
aware access policies that continuously estimate the false-negative ratio and
sometimes access caches despite negative indications. We present optimal
policies for homogeneous settings and provide approximation guarantees for our
algorithms in heterogeneous environments. We further perform an extensive
simulation study with multiple real system traces. We show that our
false-negative aware algorithms incur a significantly lower access cost than
existing approaches or match the cost of these approaches while requiring an
order of magnitude fewer resources (e.g., caching capacity or bandwidth)
Give Me Some Slack: Efficient Network Measurements
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing slack in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between W and W(1+tau) where tau is a small positive parameter. We demonstrate this model\u27s attractiveness by showing that it enables efficient algorithms to problems such as Maximum and General-Summing that require Omega(W) bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as Basic-Summing and Count-Distinct, the slack model enables a further asymptotic improvement.
The main focus of the paper is on the widely studied Basic-Summing problem of computing the sum of the last W integers from {0,1 ...,R} in a stream. While it is known that Omega(W log R) bits are needed in the exact window model, we show that approximate windows allow an exponential space reduction for constant tau.
Specifically, for tau=Theta(1), we present a space lower bound of Omega(log(RW)) bits. Additionally, we show an Omega(log (W/epsilon)) lower bound for RW epsilon additive approximations and a Omega(log (W/epsilon)+log log R) bits lower bound for (1+epsilon) multiplicative approximations. Our work is the first to study this problem in the exact and additive approximation settings. For all settings, we provide memory optimal algorithms that operate in worst case constant time. This strictly improves on the work of [Mayur Datar et al., 2002] for (1+epsilon)-multiplicative approximation that requires O(epsilon^(-1) log(RW)log log (RW)) space and performs updates in O(log (RW)) worst case time. Finally, we show asymptotic improvements for the Count-Distinct, General-Summing and Maximum problems
Scheduling Advertisement Delivery in Vehicular Networks
Vehicular users are emerging as a prime market for targeted
advertisement, where advertisements (ads) are sent from network
points of access to vehicles, and displayed to passengers only if they
are relevant to them. In this study, we take the viewpoint of a broker
managing the advertisement system, and getting paid every time a
relevant ad is displayed to an interested user. The broker selects the
ads to broadcast at each point of access so as to maximize its revenue.
In this context, we observe that choosing the ads that best fit the users’
interest could actually hurt the broker’s revenue. In light of this conflict,
we present Volfied, an algorithm allowing for conflict-free, near-optimal
ad selection with very low computational complexity. Our performance
evaluation, carried out through real-world vehicular traces, shows that
Volfied increases the broker revenue by up to 70% with provably low
computational complexity, compared to state-of-the-art alternatives.This work is supported by the European Commission through the
H2020 5G-TRANSFORMER project (Project ID 761536).En prens