Competitive Self-Stabilizing k-Clustering

Datta, Ajoy K.; Larmore, Lawrence L.; Devismes, Stéphane; Heurtefeux, Karel; Rivierre, Yvan

doi:10.1109/icdcs.2012.72

Cited by 10 publications

(13 citation statements)

References 13 publications

(2 reference statements)

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“…They present a distributed self-stabilizing algorithm to compute a distance-k dominating set D. For unit disk graphs the size of D at most 7.2552k + O(1) times the minimum possible size. The algorithm presented in this paper is similar to that in [7]. Our main contribution is a proof that, on trees, the algorithm in fact computes a minimum and not just a minimal distance-k dominating set.…”

Section: Related Workmentioning

confidence: 99%

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A Distributed Algorithm for Minimum Distance-k Domination in Trees

Turau¹,

Köhler²

2015

JGAA

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While efficient algorithms for finding minimal distance-k dominating sets exist, finding minimum such sets is NP-hard even for bipartite graphs. This paper presents a distributed algorithm to determine a minimum (connected) distance-k dominating set and a maximum distance-2k independent set of a tree T. It terminates in O(height(T)) rounds and uses O(log k) space. To the best of our knowledge this is the first distributed algorithm that computes a minimum (as opposed to a minimal) distancek dominating set for trees. The algorithm can also be applied to general graphs, albeit the distance-k dominating sets are not necessarily minimal.

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Section: Related Workmentioning

confidence: 99%

“…One of the few works for k > 1 is due to Datta et al [7]. They present a distributed self-stabilizing algorithm to compute a distance-k dominating set D. For unit disk graphs the size of D at most 7.2552k + O(1) times the minimum possible size.…”

Section: Related Workmentioning

confidence: 99%

A Distributed Algorithm for Minimum Distance-k Domination in Trees

Turau¹,

Köhler²

2015

JGAA

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“…Thereafter, r begins a top-down color-3-wave in the same way as a color-1-wave (L 12 ). A process changes its (1,4), (2,0), (2,1), (2,3), (2,4), (3,0), (3,1), (4,1), (4,2)…”

Section: Algorithm Loop(a E P)mentioning

confidence: 99%

“…These exceptions are needed because, during a color-0-wave, E(v) cannot be evaluated correctly and a process with mode A can have a neighbor with mode P . Color-incoherence preventing color waves is removed as follows: process v changes its color to 0 if some u ∈ Chi (v) satisfies (v.cl, u.cl) ∈ Illegal Pair ={ (1,3), (1,4), (2,0), (2,1), (2,3), (2,4), (3,0), (3,1), (4, 1), (4, 2)}.…”

Section: Algorithm Loop(a E P)mentioning

confidence: 99%

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A Self-Stabilizing Minimal k-Grouping Algorithm

Datta

Larmore

Masuzawa

et al. 2017

Proceedings of the 18th International Conference on Distributed Computing and Networking

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We consider the minimal k-grouping problem: given a graph G = (V, E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent self-stabilizing asynchronous distributed algorithm for this problem in the composite atomicity model of computation, assuming the network has unique process identifiers. Our algorithm works under the weakly-fair daemon. The time complexity (i.e. the number of rounds to reach a legitimate configuration) of our algorithm is O nD k where n is the number of processes in the network and D is the diameter of the network. The space complexity of each process is O((n + n false ) log n) where n false is the number of false identifiers, i.e., identifiers that do not match the identifier of any process, but which are stored in the local memory of at least one process at the initial configuration. Our algorithm guarantees that the number of groups is at most 2n/k + 1 after convergence. We also give a novel composition technique to concatenate a silent algorithm repeatedly, which we call loop composition. * This is a revised version of the conference paper [6], which appears in the proceedings of the 18th International Conference on Distributed Computing and Networking (ICDCN), ACM, 2017. This revised version slightly generalize Theorem 1. PreliminariesA connected undirected network G = (V, E) of n = |V | processes is given where n ≥ 2. Each process v has a unique identifier v.id chosen from a set ID of non-negative integers. We assume that |ID | ≤ O(n c ) holds for some constant c, thus, a process can store an identifier in O(log n) space. By an abuse of notation, we will identify each process with its identifier, and vice versa, whenever convenient. We call a member of ID a false identifier if it does not match the identifier of any process in V .We use the locally shared memory model [8]. A process is modeled by a state machine and its state is defined by the values of its variables. A process can read the values of its own and its neighbors' variables simultaneously, but can update only its own variables. An algorithm of each process v is

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Squeezing Streams and Composition of Self-stabilizing Algorithms

Altisen

Corbineau

Devismes

2019

Formal Techniques for Distributed Objects, Components, and Systems

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Composition is a fundamental tool when dealing with complex systems. We study the hierarchical collateral composition which is used to combine self-stabilizing distributed algorithms. The PADEC library is a framework developed with the Coq proof assistant and dedicated to the certification of self-stabilizing algorithms. We enrich PADEC with the composition operator and a sufficient condition to show its correctness. The formal proof of the condition leads us to develop new tools and methods on potentially infinite streams, these latter ones being used to model the algorithms' executions. The cornerstone has been the definition of the function Squeeze which removes duplicates from streams.

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Competitive Self-Stabilizing k-Clustering

Cited by 10 publications

References 13 publications

A Distributed Algorithm for Minimum Distance-k Domination in Trees

A Distributed Algorithm for Minimum Distance-k Domination in Trees

A Self-Stabilizing Minimal k-Grouping Algorithm

Squeezing Streams and Composition of Self-stabilizing Algorithms

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