A Self-Stabilizing O(n)-Round k-Clustering Algorithm

Datta, Ajoy K.; Devismes, Stéphane; Larmore, Lawrence L.

doi:10.1109/srds.2009.13

Cited by 19 publications

(27 citation statements)

References 19 publications

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“…Stabilizing algorithms that contain the effects of a single fault are presented in . A stabilizing algorithm for clustering a network is proposed in . An optimal snap‐stabilizing PIF algorithm for un‐oriented trees is presented in .…”

Section: Preliminaries and Backgroundmentioning

confidence: 99%

An optimal inherently stabilizing routing algorithm for star P2P overlay networks

Karaata

Alsulaiman

2016

Concurrency and Computation

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Summary Star graphs possess many desirable properties such as scalable node degrees and diameters, which are essential to facilitate reduced routing table sizes and low maximum path length for routing in large P2P networks. In addition, because a large number of disjoint paths are available and each data/replica in an n‐star can be placed in an (n − 1)‐star, load balancing and alleviation of network bottlenecks can be implemented in star P2P overlay networks. Therefore, star networks have been proposed as viable alternatives to existing overlay topologies for large P2P networks. In this paper, we propose an optimal stabilizing and inherently stabilizing algorithm for routing messages over all disjoint paths between two peers in a star P2P overlay network. The algorithm is optimal in terms of its time complexity in rounds and the length of the longest path traversed by the messages, and fault tolerant due to being stabilizing and inherently stabilizing, allowing the system to withstand transient faults. The algorithm can be used to increase network reliability and survivability in P2P networks. In addition, the usage of all disjoint paths to route messages between two peers leads to increased network bandwidth while distributing the communication overhead across the network and eliminating network bottlenecks in P2P networks. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Preliminaries and Backgroundmentioning

confidence: 99%

An optimal inherently stabilizing routing algorithm for star P2P overlay networks

Karaata

Alsulaiman

2016

Concurrency and Computation

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“…There are several known asynchronous self-stabilizing distributed algorithms for finding a k-clustering of a network, e.g., [7,6,3]. The solution in [7] stabilizes in O(k) rounds using O(k log n) space per process.…”

Section: Introductionmentioning

confidence: 99%

“…The solution in [7] stabilizes in O(k) rounds using O(k log n) space per process. The algorithm given in [6] stabilizes in O(n) rounds using O(log n) space per process. The algorithm given in [3] stabilizes in O(kn) rounds using O(k log n) space per process.…”

Section: Introductionmentioning

confidence: 99%

Competitive self-stabilizing k-clustering

Datta

Devismes

Heurtefeux

et al. 2016

Theoretical Computer Science

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A k-cluster of a graph is a connected non-empty subgraph C of radius at most k, i.e., all members of C are within distance k of a particular node of C, called the clusterhead of C. A k-clustering of a graph is a partitioning of the graph into distinct k-clusters. Finding a minimum cardinality k-clustering is known to be N P-hard. In this paper, we propose a silent self-stabilizing asynchronous distributed algorithm for constructing a k-clustering of any connected network with unique IDs. Our algorithm stabilizes in O(n) rounds, using O(log n) space per process, where n is the number of processes. In the general case, our algorithm constructs O( n k ) k-clusters. If the network is a Unit Disk Graph (UDG), then our algorithm is 7.2552k + O(1)-competitive, that is, the number of kclusters constructed by the algorithm is at most 7.2552k + O(1) times the minimum possible number of k-clusters in any k-clustering of the same network. More generally, if the network is an Approximate Disk Graph (ADG) with approximation ratio λ, then our algorithm is 7.2552λ 2 k + O(λ)-competitive. Our solution is based on the self-stabilizing construction of a data structure called the MIS Tree, a spanning tree of the network whose processes at even levels form a maximal independent set of the network. The MIS tree construction is the time bottleneck of our k-clustering algorithm, as it takes Θ(n) rounds in the worst case, while the remainder of the algorithm takes O(D) rounds, where D is the diameter of the network. We would like to improve that time to be O(D), but we show that our distributed MIS tree construction is a P-complete problem.

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“…Many 1-hop clustering algorithms have been proposed in the literature. A large number of them are self-stabilizing [2], [7], [10], [6], [9], [15], [19]. There are also robust self-stabilizing clustering algorithms [16], [13], and selfstabilizing with safe convergence [18].…”

Section: Introductionmentioning

confidence: 99%

Self-Stabilizing Computation and Preservation of Knowledge of Neighbor Clusters

Johnen

Mekhaldi

2011

2011 IEEE Fifth International Conference on Self-Adaptive and Self-Organizing Systems

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Abstract-The area of self-stabilization in large scale networks has been received increasing attention among researchers, since self-stabilization provides a foundation for self-properties, including self-healing, self-organizing and self-adaptive. This paper makes contributions in two areas. First, we describe a new extended approach of selfstabilization, called self-stabilization with service guarantee. Second, we propose a self-stabilizing protocol computing and preserving the knowledge of neighbor clusters, called CNK. A cluster-head maintains about each neighbor cluster: the identity of its head, paths leading to it, and the list of members. The most interesting property of CNK is the service guarantee during the stabilization phase. CNK quickly provides, in at most 4 rounds, the following minimal useful service: "each cluster-head knows valid paths leading to heads of all its neighbor clusters". CNK protocol preserves the minimal service despite changes in the clustering structure (creation of new clusters, restructuring or crumbling of existing clusters). The knowledge of neighbor clusters is thus highly available. This knowledge is enough to allow the continuity functioning of hierarchical protocols as hierarchical routing protocols.

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A Self-Stabilizing O(n)-Round k-Clustering Algorithm

Cited by 19 publications

References 19 publications

An optimal inherently stabilizing routing algorithm for star P2P overlay networks

An optimal inherently stabilizing routing algorithm for star P2P overlay networks

Competitive self-stabilizing k-clustering

Self-Stabilizing Computation and Preservation of Knowledge of Neighbor Clusters

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