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In the matching problem, each node maintains a pointer to one of its neighboror to $null$, and a maximal matching is computed when each node points eitherto a neighbor that itself points to it (they are then called married), or to$null$, in which case no neighbor can also point to $null$. This paper presentsa self-stabilizing distributed algorithm to compute a maximal matching in thelink-register model under read/write atomicity, with complexity{$O(n\Delta^3)$} moves under the adversarial distributed daemon, where $\Delta$is the maximum degree of the graph.

A self-stabilizing algorithm for maximal matching in link-register model in $O(n\Delta^3)$ moves