2019 Preprint**Abstract:** 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(log 2 n) 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(log 2 n) memory, using approximation and parametrized complexity.More specifically, ou…

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“…This can be problematic if we want to build the certificates in a distributed manner without exceeding some space limit. A recent preprint [2] tackles the problem of how to construct the labels to a get an optimal space self-stabilizing algorithm, and solve this problem by allowing the nodes to check the size of their labels.…”

confidence: 99%

“…This is due to Korman and Kutten who describe it in concise and formal manner in [7]. In this note, we propose a more intuitive description of the result, as well as a gentle introduction to the problem.This note originates from a careful reading of [7], while working on [2]. Comments are most welcome.…”

mentioning

confidence: 99%

“…A general open problem is to determine which results from distributed decision can be used for self-stabilization. A more concrete one is the following: in [8] the self-stabilizing algorithm for MST first computes the solution, and then computes the certificates, and this is unusual: algorithms usually compute the solution and its certification at the same time. The paper [8] provides some elements showing that this form might be necessary, but no complete proof is known.…”

confidence: 99%

“…Second, many lower bounds work only in a ring, which tells us little about denser topologies. Third, the only result we have with other parameters is the Θ(log n log W ) bound for minimum spanning tree [32], where W is the maximum edge weight; and this parametrization led to improvements of self-stabilizing algorithms [8].…”

confidence: 99%