In this paper we show that approximation can help reduce
the space used for self-stabilization. In the classic 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 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.