1 research outputs found
Succinct Approximate Rank Queries
We consider the problem of summarizing a multi set of elements in under the constraint that no element appears more than
times. The goal is then to answer \emph{rank} queries --- given , how many elements in the multi set are smaller than ? ---
with an additive error of at most and in constant time. For this
problem, we prove a lower bound of
bits
and provide a \emph{succinct} construction that uses bits. Next, we generalize our data structure to
support processing of a stream of integers in , where upon
a query for some we provide a -additive approximation for the
sum of the \emph{last} elements. We show that this too can be done using
bits and in constant time. This yields the
first sub linear space algorithm that computes approximate sliding window sums
in time, where the window size is given at the query time; additionally,
it requires only more space than is needed for a fixed window size