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  A lower bound for linear approximate compaction

Chaudhuri, S.(1993). A lower bound for linear approximate compaction (MPI-I-93-146). Saarbrücken: Max-Planck-Institut für Informatik.

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Chaudhuri, Shiva1, Author           
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: The {\em $\lambda$-approximate compaction} problem is: given an input array of $n$ values, each either 0 or 1, place each value in an output array so that all the 1's are in the first $(1+\lambda)k$ array locations, where $k$ is the number of 1's in the input. $\lambda$ is an accuracy parameter. This problem is of fundamental importance in parallel computation because of its applications to processor allocation and approximate counting. When $\lambda$ is a constant, the problem is called {\em Linear Approximate Compaction} (LAC). On the CRCW PRAM model, %there is an algorithm that solves approximate compaction in $\order{(\log\log n)^3}$ time for $\lambda = \frac{1}{\log\log n}$, using $\frac{n}{(\log\log n)^3}$ processors. Our main result shows that this is close to the best possible. Specifically, we prove that LAC requires %$\Omega(\log\log n)$ time using $\order{n}$ processors. We also give a tradeoff between $\lambda$ and the processing time. For $\epsilon < 1$, and $\lambda = n^{\epsilon}$, the time required is $\Omega(\log \frac{1}{\epsilon})$.

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Language(s): eng - English
 Dates: 1993
 Publication Status: Issued
 Pages: 12 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Identifiers: URI: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/93-146
Report Nr.: MPI-I-93-146
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Title: Research Report / Max-Planck-Institut für Informatik
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