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(21 citation statements)

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“…By non-rooted components detection, we mean that every process that belongs to a connected component which does not contain a root should eventually take a special state notifying that it detects the absence of a root. This instance stabilizes in O (n maxCC •n) moves, which matches the best known step complexity for spanning tree construction [12] with explicit parent pointers.…”

confidence: 69%

“…By non-rooted components detection, we mean that every process that belongs to a connected component which does not contain a root should eventually take a special state notifying that it detects the absence of a root. This instance stabilizes in O (n maxCC •n) moves, which matches the best known step complexity for spanning tree construction [12] with explicit parent pointers.…”

confidence: 69%

“…Silent self-stabilizing algorithms that construct spanning trees of arbitrary topologies in arbitrary connected and rooted networks are given in [12,34]. The solution proposed in [12] stabilizes in at most 4 • n rounds and 5 • n 2 steps, while the algorithm given in [34] stabilizes in n • D moves. However, its round complexity is not analyzed and the parent of a process is not computed explicitly.…”

confidence: 99%

“…There is a huge literature on the self-stabilizing construction of various kinds of trees, including spanning trees (ST) [20], [22], [53], breadth-first search (BFS) trees [1], [3], [18], [24], [30], [42], [48], depth-first search (DFS) trees [21], [23], [24], [43], minimum-weight spanning trees (MST) [13], [17], [39], [41], [51], shortest-path spanning trees [38], [44], minimumdiameter spanning trees [12], minimum-degree spanning trees (MDST) [16], etc. Some of these constructions are even silent, with optimal space-complexity.…”

confidence: 99%

“…There is an extensive, literature on self-stabilizing construction of various kinds of trees, including spanning trees (ST) [15,39], breadth-first search (BFS) trees [1,12,16,24,34], depth-first search (DFS) trees [14,35], minimum-weight 1 spanning trees (MST) [38,6], shortest-path spanning trees [30,36], minimumdegree spanning trees [9], Steiner Tree [8], etc. A survey on self-stabilizing distributed protocols for spanning tree construction can be found in [27].…”

confidence: 99%