Silent MST approximation for tiny memory
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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(^2n) 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(^2n) 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( n · 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( n) for an n-approximation, to memory O(^2n) for exact solutions, with for example memory O( n n) for a 2-approximation.
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