# MPI-I-93-146

## A lower bound for linear approximate compaction

### Chaudhuri, Shiva

**MPI-I-93-146**. October** **1993, 12 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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 $\Omega(\log \frac{1}{\epsilon})$.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1993-146

**BibTeX**
`@TECHREPORT{``Chaudhuri93b``,`

` AUTHOR = {Chaudhuri, Shiva},`

` TITLE = {A lower bound for linear approximate compaction},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-93-146},`

` MONTH = {October},`

` YEAR = {1993},`

` ISSN = {0946-011X},`

`}`