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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > WIDAD MACHMOUCHI:
All reports by Author Widad Machmouchi:

TR13-127 | 15th September 2013
Paul Beame, Raphael Clifford, Widad Machmouchi

Element Distinctness, Frequency Moments, and Sliding Windows

We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. In particular, we develop a randomized algorithm for the element distinctness problem whose time $T$ and space $S$ ... more >>>


TR12-178 | 18th December 2012
Paul Beame, Raphael Clifford, Widad Machmouchi

Sliding Windows With Limited Storage

Revisions: 1

We consider time-space tradeoffs for exactly computing frequency
moments and order statistics over sliding windows.
Given an input of length $2n-1$, the task is to output the function of
each window of length $n$, giving $n$ outputs in total.
Computations over sliding windows are related to direct sum problems
except ... more >>>


TR10-104 | 29th June 2010
Paul Beame, Widad Machmouchi

Making RAMs Oblivious Requires Superlogarithmic Overhead

Revisions: 3 , Comments: 1

We prove a time-space tradeoff lower bound of $T =
\Omega\left(n\log(\frac{n}{S}) \log \log(\frac{n}{S})\right) $ for
randomized oblivious branching programs to compute $1GAP$, also
known as the pointer jumping problem, a problem for which there is a
simple deterministic time $n$ and space $O(\log n)$ RAM (random
access machine) algorithm.

In ... more >>>




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