  In this paper we show that approximation can help reduce the space used for
self-stabilization. In the classic \emph{state model}, where the nodes of a
network communicate by reading the states of their neighbors, an important
measure of efficiency is the space: the number of bits used at each node to
encode the state. In this model, a classic requirement is that the algorithm
has to be \emph{silent}, that is, after stabilization the states should not
change anymore. We design a silent self-stabilizing algorithm for the problem
of minimum spanning tree, that has a trade-off between the quality of the
solution and the space needed to compute it.
