In network distributed computing, minimum spanning tree (MST) is one of the
key problems, and silent self-stabilization one of the most demanding
fault-tolerance properties. For this problem and this model, a polynomial-time
algorithm with O(log2n) memory is known for the state model. This is
memory optimal for weights in the classic [1,poly(n)] range (where n
is the size of the network). In this paper, we go below this O(log2n)
memory, using approximation and parametrized complexity.
More specifically, our contributions are two-fold. We introduce a second
parameter~s, which is the space needed to encode a weight, and we design a
silent polynomial-time self-stabilizing algorithm, with space O(lognâ s). In turn, this allows us to get an approximation algorithm for the problem,
with a trade-off between the approximation ratio of the solution and the space
used. For polynomial weights, this trade-off goes smoothly from memory O(logn) for an n-approximation, to memory O(log2n) for exact solutions,
with for example memory O(lognloglogn) for a 2-approximation