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A stabilizing deterministic message-passing skip list.
, 2011
"... Abstract. We present Corona, a deterministic self-stabilizing algorithm for skip list construction in structured overlay networks. Corona operates in the low-atomicity message-passing asynchronous system model. Corona requires constant process memory space for its operation and, therefore, scales w ..."
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Abstract. We present Corona, a deterministic self-stabilizing algorithm for skip list construction in structured overlay networks. Corona operates in the low-atomicity message-passing asynchronous system model. Corona requires constant process memory space for its operation and, therefore, scales well. We prove the general necessary conditions limiting the initial states from which a self-stabilizing structured overlay network in message-passing system can be constructed. The conditions require that initial state information has to form a weakly connected graph and it should only contain identifiers that are present in the system. We formally describe Corona and rigorously prove that it stabilizes from an arbitrary initial state subject to the necessary conditions. We extend Corona to construct a skip graph.
Snap-Stabilizing Linear Message Forwarding
- in "12th International Symposium Stabilization, Safety, and Security of Distributed Systems (SSS
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Rigorous Performance Evaluation of Self-Stabilization Using Probabilistic Model Checking
- In SRDS. IEEE
, 2013
"... Abstract—We propose a new metric for effectively and accu-rately evaluating the performance of self-stabilizing algorithms. Self-stabilization is a versatile category of fault-tolerance that guarantees system recovery to normal behavior within a finite number of steps, when the state of the system i ..."
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Abstract—We propose a new metric for effectively and accu-rately evaluating the performance of self-stabilizing algorithms. Self-stabilization is a versatile category of fault-tolerance that guarantees system recovery to normal behavior within a finite number of steps, when the state of the system is perturbed by transient faults (or equally, the initial state of the system can be some arbitrary state). The performance of self-stabilizing algorithms is conventionally characterized in the literature by asymptotic computation complexity. We argue that such characterization of performance is too abstract and does not reflect accurately the realities of deploying a distributed algorithm in practice. Our new metric for characterizing the performance of self-stabilizing algorithms is the expected mean value of recovery time. Our metric has several crucial features. Firstly, it encodes accurate average case speed of recovery. Secondly, we show that our evaluation method can effectively incorporate several other parameters that are of importance in practice and have no place in asymptotic computation complexity. Examples include the type of distributed scheduler, likelihood of occurrence of faults, the impact of faults on speed of recovery, and network topology. We utilize a deep analysis technique, namely, probabilistic model checking to rigorously compute our proposed metric. All our claims are backed by detailed case studies and experiments. Keywords-Self-stabilization; Performance evaluation; formal methods I.
Self-Stabilizing Balancing Algorithm for Containment-Based Trees
, 2012
"... Abstract—Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts. In addition to their versatility, their balanced sh ..."
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Abstract—Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts. In addition to their versatility, their balanced shape ensures an overall satisfactory performance. Recently, it has been shown that their distributed implementations can be faultresilient. However, this robustness is achieved at the cost of unbalancing the structure. While the structure remains correct in terms of searchability, its performance can be significantly decreased. In this paper, we propose a distributed self-stabilizing algorithm to balance containment-based trees. Index Terms—self-stabilization, balancing algorithms, containment-based trees I.
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"... network, and which preserves the static network’s O(log n) routing time and constant node degrees. Moreover, the LDB network is self-stabilizing in the sense that it can recover from any case in which the topology is still weakly connected. Recall that a directed graph G is called weakly connected i ..."
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network, and which preserves the static network’s O(log n) routing time and constant node degrees. Moreover, the LDB network is self-stabilizing in the sense that it can recover from any case in which the topology is still weakly connected. Recall that a directed graph G is called weakly connected if for any pair of nodes v, w there is a path in G from v to w when considering all edges to be undirected. Other dynamic variants of the De Bruijn network have been proposed in the literature before (e.g., [16]), but none of them is self-stabilizing. This paper is organized as follows. In Section 2, we present the related work in the literature and Section 3 defines the structure of the LDB network. We then present our routing algorithm in Section 4 and prove its logarithmic bound. Section 5 presents the self-stabilization results for the LDB while Section 6 describes and analyzes join and leave operations. Section 7 concludes the paper and also presents some lines for future work. 2 Related Work Our work expands on that of Naor and Wieder in [16]. Both our construction
