190 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
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