Self-Stabilizing Small k-Dominating Sets

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

doi:10.15803/ijnc.3.1_116

Cited by 23 publications

(21 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are a variety of techniques to compose two or more self-stabilizing algorithms in the literature [9,10,2,13,4,14,15], such as fair-composition [10] and parallel composition [9], but none of them enables an unbounded number of repetitions of the same algorithm, such as ours.…”

Section: Related Workmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

A Self-Stabilizing Minimal k-Grouping Algorithm

Datta

Larmore

Masuzawa

et al. 2017

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

View full text Add to dashboard Cite

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

show abstract

Section: Related Workmentioning

confidence: 99%

“…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%

Section: Algorithm Loop(a E P)mentioning

confidence: 99%

See 1 more Smart Citation

A Self-Stabilizing Minimal k-Grouping Algorithm

Datta

Larmore

Masuzawa

et al. 2017

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

View full text Add to dashboard Cite

show abstract

“…The protocol of [6] requires O(log(n) + k.log(n/k)) bits per node. The protocol of [5] builds competitive kdominating sets : the obtained dominating set contains at most 1+ (n−1)/(k+1) nodes.…”

Section: Introductionmentioning

confidence: 99%

Memory Efficient Self-Stabilizing k-Independent Dominating Set Construction

Johnen

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We propose a memory efficient self-stabilizing protocol building k-independent dominating sets. A k-independent dominating set is a k-independent set and a kdominating set. A set of nodes, I, is k-independent if the distance between any pair of nodes in I is at least k + 1. A set of nodes, D, is a k-dominating if every node is within distance k of a node of D. Our algorithm, named SID, is silent; it converges under the unfair distributed scheduler (the weakest scheduling assumption). We established that any k-independent sets contains at most (2n)/(k + 2) nodes, n being the network size. The protocol SID is memory efficient : it requires only 2log((k + 1)n + 1) + 1 bits per node. The correctness and the termination of the protocol SID is proven. The computation of the convergence time of the protocol SID is opened question.

show abstract

“…Starting from an arbitrary configuration, a silent algorithm converges within finite time to a configuration from which all communication variables are constant. This class of self-stabilizing algorithms is important, as self-stabilizing algorithms building distributed data structures (such as spanning tree or clustering) often achieve the silent property, and these silent self-stabilizing data structures are widely used as basic building blocks for more complex self-stabilizing solutions, e.g., [19,20].Using a usual proof scheme, the certified proof consists of two main parts, one dealing with termination and the other with partial correctness.For the termination part, we developed tools on potential functions and termination at a fine-grained level. Precisely, we define a potential function as a multiset containing a local potential per node.…”

mentioning

confidence: 99%

A Framework for Certified Self-Stabilization

Altisen

Corbineau

Devismes

2016

Formal Techniques for Distributed Objects, Components, and Systems

Self Cite

View full text Add to dashboard Cite

Abstract. We propose a general framework to build certified proofs of distributed selfstabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model in the self-stabilizing area. We then validate our framework by certifying a non trivial part of an existing silent self-stabilizing algorithm which builds a k-clustering of the network. We also certify a quantitative property related to the output of this algorithm. Precisely, we show that the computed k-clustering contains at most n−1 k+1 + 1 clusterheads, where n is the number of nodes in the network. To obtain these results, we also developed a library which contains general tools related to potential functions and cardinality of sets.

show abstract

Self-Stabilizing Small k-Dominating Sets

Cited by 23 publications

References 27 publications

A Self-Stabilizing Minimal k-Grouping Algorithm

A Self-Stabilizing Minimal k-Grouping Algorithm

Memory Efficient Self-Stabilizing k-Independent Dominating Set Construction

A Framework for Certified Self-Stabilization

Contact Info

Product

Resources

About