An Efficient Silent Self-Stabilizing Algorithm for 1-Maximal Matching in Anonymous Networks

A Self-Stabilizing Algorithm for Maximal Matching in Link-Register Model

“…This implies that if (s, t) is in the state (Y ou, α, β), then r st = (Y ou, α) and r ts = (Y ou, β). Thus, according to Definition 3, the only remaining possibilities for (α, β) are (2, 0), (0, 2), (1, 0) and (1,2). In all of these cases, s is activable for a Reset rule which contradicts the fact that C is a stable configuration.…”

“…Self-stabilizing algorithms for computing maximal matching have been designed in various models (anonymous network [1] or not [14], weighted or unweighted, see [7] for a survey). For an unweighted graph, Hsu and Huang [9] gave the first self-stabilizing algorithm and proved a bound of O(n 3 ) on the number of moves under a sequential adversarial daemon.…”

“…The presented algorithm is based on the algorithm by Manne et al [11] written under the state model. A marriage is contracted in two phases: (1) the selection of the edge to add to the matching and (2) the confirmation or the lock of the edge in the matching in three steps.…”