Sofya Raskhodnikova, Dana Ron, Ronitt Rubinfeld, Amir Shpilka, Adam Smith

We raise the question of approximating compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and Lempel-Ziv (LZ), and present algorithms and lower bounds for approximating compressibility with respect to ... more >>>

Paul Beame, Trinh Huynh

Recently, an extension of the standard data stream model has been introduced in which an algorithm can create and manipulate multiple read/write streams in addition to its input data stream. Like the data stream model, the most important parameter for this model is the amount of internal memory used by ... more >>>

Joshua Brody, Amit Chakrabarti

The Gap-Hamming-Distance problem arose in the context of proving space

lower bounds for a number of key problems in the data stream model. In

this problem, Alice and Bob have to decide whether the Hamming distance

between their $n$-bit input strings is large (i.e., at least $n/2 +

\sqrt n$) ...
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Paul Beame, Raphael Clifford, Widad Machmouchi

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 ...
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Paul Beame, Raphael Clifford, Widad Machmouchi

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 >>>

Omri Weinstein, David Woodruff

We study $k$-party set disjointness in the simultaneous message-passing model, and show that even if each element $i\in[n]$ is guaranteed to either belong to all $k$ parties or to at most $O(1)$ parties in expectation (and to at most $O(\log n)$ parties with high probability), then $\Omega(n \min(\log 1/\delta, \log ... more >>>

Amit Chakrabarti, Sagar Kale

We develop a paradigm for studying multi-player deterministic communication,

based on a novel combinatorial concept that we call a {\em strong fooling

set}. Our paradigm leads to optimal lower bounds on the per-player

communication required for solving multi-player $\textsc{equality}$

problems in a private-message setting. This in turn gives a ...
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