A New Polynomial Silent Stabilizing Spanning-Tree Construction Algorithm

Cournier, Alain

doi:10.1007/978-3-642-11476-2_12

Cited by 14 publications

(21 citation statements)

References 13 publications

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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.…”

Section: Contributionsupporting

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.…”

Section: Related Workmentioning

confidence: 99%

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

Devismes

Ilcinkas

Johnen³

2019

Proceedings of the 20th International Conference on Distributed Computing and Networking

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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.

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Section: Contributionsupporting

confidence: 69%

Section: Related Workmentioning

confidence: 99%

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

Devismes

Ilcinkas

Johnen³

2019

Proceedings of the 20th International Conference on Distributed Computing and Networking

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“…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.…”

Section: Related Workmentioning

confidence: 99%

Space-Optimal Time-Efficient Silent Self-Stabilizing Constructions of Constrained Spanning Trees

Blin

Fraigniaud

2015

2015 IEEE 35th International Conference on Distributed Computing Systems

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International audienceSelf-stabilizing algorithms are distributed algorithms supporting transient failures. Starting from any configuration, they allow the system to detect whether the actual configuration is legal, and, if not, they allow the system to eventually reach a legal configuration. In the context of network computing, it is known that, for every task, there is a self-stabilizing algorithm solving that task, with optimal space-complexity, but converging in an exponential number of rounds. On the other hand, it is also known that, for every task, there is a self-stabilizing algorithm solving that task in a linear number of rounds, but with large space-complexity. It is however not known whether for every task there exists a self-stabilizing algorithm that is simultaneously space-efficient and time-efficient. In this paper, we make a first attempt for answering the question of whether such an efficient algorithm exists for every task, by focussing on constrained spanning tree construction tasks. We present a general roadmap for the design of silent space-optimal self-stabilizing algorithms solving such tasks, converging in polynomially many rounds under the unfair scheduler. By applying our roadmap to the task of constructing minimum-weight spanning tree (MST), and to the task of constructing minimum-degree spanning tree (MDST), we provide algorithms that outperform previously known algorithms designed and optimized specifically for solving each of these two tasks

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“…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].…”

Section: Introductionmentioning

confidence: 99%

A self-stabilizing memory efficient algorithm for the minimum diameter spanning tree under an omnipotent daemon

Blin

Boubekeur

Dubois³

2018

Journal of Parallel and Distributed Computing

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Routing protocols are at the core of distributed systems performances, especially in the presence of faults. A classical approach to this problem is to build a spanning tree of the distributed system. Numerous spanning tree construction algorithms depending on the optimized metric exist (total weight, height, distance with respect to a particular process,. . .) both in fault-free and faulty environments. In this paper, we aim at optimizing the diameter of the spanning tree by constructing a minimum diameter spanning tree. We target environments subject to transient faults (i.e. faults of finite duration). Hence, we present a self-stabilizing algorithm for the minimum diameter spanning tree construction problem in the state model. Our protocol has the following attractive features. It is the first algorithm for this problem that operates under the unfair and distributed adversary (or daemon). In other words, no restriction is made on the asynchronous behavior of the system. Second, our algorithm needs only O(log n) bits of memory per process (where n is the number of processes), that improves the previous result by a factor n. These features are not achieved to the detriment of the convergence time, which stays polynomial.

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A New Polynomial Silent Stabilizing Spanning-Tree Construction Algorithm

Cited by 14 publications

References 13 publications

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

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

Space-Optimal Time-Efficient Silent Self-Stabilizing Constructions of Constrained Spanning Trees

A self-stabilizing memory efficient algorithm for the minimum diameter spanning tree under an omnipotent daemon

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