  We introduce a new algebraic sieving technique to detect constrained
multilinear monomials in multivariate polynomial generating functions given by
an evaluation oracle. As applications of the technique, we show an
$O^*(2^k)$-time polynomial space algorithm for the $k$-sized Graph Motif
problem. We also introduce a new optimization variant of the problem, called
Closest Graph Motif and solve it within the same time bound. The Closest Graph
Motif problem encompasses several previously studied optimization variants,
like Maximum Graph Motif, Min-Substitute Graph Motif, and Min-Add Graph Motif.
Finally, we provide a piece of evidence that our result might be essentially
tight: the existence of an $O^*((2-\epsilon)^k)$-time algorithm for the Graph
Motif problem implies an $O((2-\epsilon')^n)$-time algorithm for Set Cover.
