  We exhibit an algorithm to solve the following extension problem: Given a
finite set $E \subset \mathbb{R}^n$ and a function $f: E \rightarrow
\mathbb{R}$, compute an extension $F$ in the Sobolev space
$L^{m,p}(\mathbb{R}^n)$, $p>n$, with norm having the smallest possible order of
magnitude, and secondly, compute the order of magnitude of the norm of $F$.
Here, $L^{m,p}(\mathbb{R}^n)$ denotes the Sobolev space consisting of functions
on $\mathbb{R}^n$ whose $m$th order partial derivatives belong to
$L^p(\mathbb{R}^n)$. The running time of our algorithm is at most $C N \log N$,
where $N$ denotes the cardinality of $E$, and $C$ is a constant depending only
on $m$,$n$, and $p$.
