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\title{
\begin{flushleft}
\vspace{-0.9in}
\scriptsize {\em
Working paper, January, 1997.
}
\end{flushleft}
\vspace{0.4in}
\Large\bf 
Barriers for fun and profit
}

\author{
\begin{tabular}[c]{ c@{\extracolsep{2em}} c} 
Thomas E. Warfel & David R. O'Hallaron\\
\\
{Univ. of Pgh. Medical Center} & {School of Computer Science} \\ 
{Pittsburgh, PA xxxxx}  	& {Carnegie Mellon University} \\ 
				& {Pittsburgh, PA 15213}       \\
\end{tabular}
} 
\date{}

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\unmarkedfootnote{
This research was sponsored in part by the Advanced Research Projects
Agency/CSTO monitored by SPAWAR under contract N00039-93-C-0152, 
in part by the National Science Foundation under
Grant CMS-9318163, and in part by a grant from the Intel Corporation.

The views and conclusions contained in this document are those of the
authors and should not be interpreted as representing the official
policies, either express or implied, of the U.S. government.
}

\begin{abstract}
Here is the abstract.
\end{abstract}

\section{Introduction}
\label{sec:intro}
To compute ${\bf y = Kx}$ on a set of processors, we must consider the
data distribution by which vectors and matrices are stored.  The
vectors ${\bf x}$ and ${\bf y}$ are stored in a distributed fashion
according to the mapping of nodes to processors induced by the partition
of elements among processors.  If a node $i$ resides in several
processors (because $i$ is a vertex of several elements mapped to
different processors), the values $x_i$ and $y_i$ are replicated on those
processors.  The matrix ${\bf K}$ is distributed so that $K_{ij}$
resides on any processor on which nodes $i$ and $j$ both reside.
Figure~\ref{fig:cutmatrix} demonstrates this method of distributing data.
\begin{figure}[htbp]
\epsfxsize=2in
\centerline{\epsfbox{cutmatrix.epsf}}
\caption{A finite element mesh}
\label{fig:cutmatrix} 
\end{figure}

The processors of modern parallel and distributed computer systems are
commodity microprocessors whose peak performance is doubling
every 18 months or so. Clearly, communication performance will have to
improve as processor performance increases, but the question is how
much and in what respects.  It is crucial to understand communication
requirements because some parts of the communication system will not
be commodity, and are therefore expensive.

\section{Conclusions}
Here are the conclusions.

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