A Self-Stabilizing Memory Efficient Algorithm for the Minimum Diameter Spanning Tree under an Omnipotent Daemon

Blin, Lélia; Boubekeur, Fadwa; Dubois, Swan

doi:10.1109/ipdps.2015.44

Cited by 6 publications

(3 citation statements)

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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

Fraigniaud²

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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Section: Related Workmentioning

confidence: 99%

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

Blin

Fraigniaud²

2015

2015 IEEE 35th International Conference on Distributed Computing Systems

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“…On the other hand, growing and merging trees is the main technique for designing self-stabilizing leader election algorithms in networks, as the leader is often the root of an inward tree [3,4,2,9]. To the best of our knowledge, all algorithms that do not assume a pre-existing leader [3,4,2,8] for tree-construction use Ωplog nq bits per node. This high space-complexity is due to the implementation of two main techniques, used by all algorithms, and recalled below.…”

Section: Introductionmentioning

confidence: 99%

Compact Self-Stabilizing Leader Election for General Networks

Blin

Tixeuil²

2018

Lecture Notes in Computer Science

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We present a self-stabilizing leader election algorithm for arbitrary networks, with spacecomplexity Opmaxtlog ∆, log log nuq bits per node in n-node networks with maximum degree ∆. This space complexity is sub-logarithmic in n as long as ∆ " n op1q . The best space-complexity known so far for arbitrary networks was Oplog nq bits per node, and algorithms with sublogarithmic space-complexities were known for the ring only. To our knowledge, our algorithm is the first algorithm for self-stabilizing leader election to break the Ωplog nq bound for silent algorithms in arbitrary networks. Breaking this bound was obtained via the design of a (nonsilent) self-stabilizing algorithm using sophisticated tools such as solving the distance-2 coloring problem in a silent self-stabilizing manner, with space-complexity Opmaxtlog ∆, log log nuq bits per node. Solving this latter coloring problem allows us to implement a sub-logarithmic encoding of spanning trees -storing the IDs of the neighbors requires Ωplog nq bits per node, while we encode spanning trees using Opmaxtlog ∆, log log nuq bits per node. Moreover, we show how to construct such compactly encoded spanning trees without relying on variables encoding distances or number of nodes, as these two types of variables would also require Ωplog nq bits per node. * Sorbonne Universités, UPMC Univ Paris 06, CNRS, Université d'Evry-Val-d'Essonne, LIP6 UMR 7606, 4 place Jussieu 75005, Paris. † Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606, 4 place Jussieu 75005, Paris.

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“…On the other hand, growing and merging trees is the main technique for designing self-stabilizing leader election algorithms in networks, as the leader is often the root of an inward tree [3,4,2]. To the best of our knowledge, all algorithms that do not assume a pre-existing leader [3,4,2,10] for tree-construction use Ωplog nq bits per node. This high space-complexity is due to the implementation of two main techniques, used by all algorithms, and recalled below.…”

Section: Related Workmentioning

confidence: 99%