Silent self-stabilizing scheme for spanning-tree-like constructions

Abstract

In this paper, we propose a general scheme, called Algorithm STlC, to compute spanning-tree-like data structures on arbitrary networks. STlC is self-stabilizing and silent and, despite its generality, is also efficient. It is written in the locally shared memory model with composite atomicity assuming the distributed unfair daemon, the weakest scheduling assumption of the model. Its stabilization time is in O (n maxCC) rounds, where n maxCC is the maximum number of processes in a connected component. We also exhibit polynomial upper bounds on its stabilization time in steps and process moves holding for large classes of instantiations of Algorithm STlC. We illustrate the versatility of our approach by proposing several such instantiations that efficiently solve classical problems such as leader election, as well as, unconstrained and shortest-path spanning tree constructions.

Acyclic Strategy for Silent Self-stabilization in Spanning Forests

“…In many of those related works, the assumption about the existence of a directed (spanning) tree in the network has to be considered as an intermediate assumption, since this structure has to be built by an underlying algorithm. Now, there are several silent selfstabilizing spanning tree constructions that are efficient in both rounds and moves, e.g., [32]. Thus, both algorithms, i.e., the one that builds the tree and the one that computes on this tree, have to be carefully composed to obtain a general composite algorithm where, the stabilization time is keeped both asymptotically optimal in rounds and polynomial in moves.…”

“…To our knowledge, until now, only two works [31,32] conciliate general schemes for stabilization and efficiency in both moves and rounds. In [31], Cournier et al propose a general scheme for snap-stabilizing wave, henceforth non-silent, algorithms in arbitrary connected and rooted networks.…”

“…Using their approach, one can obtain snap-stabilizing algorithms that execute each wave in polynomial number of rounds and moves. In [32], authors propose a general scheme to compute, in a linear number of rounds, spanning directed treelike data structures on arbitrary networks. They also exhibit polynomial upper bounds on its stabilization time in moves holding for large classes of instantiations of their scheme.…”

“…They also exhibit polynomial upper bounds on its stabilization time in moves holding for large classes of instantiations of their scheme. Hence, our approach is complementary to [32].…”