## Abstract

Self-stabilization ensures automatic recovery from an arbitrary state; we define self-organization as a property of algorithms which display local attributes. More precisely, we say that an algorithm is self-organizing if (1) it converges in sublinear time and (2) reacts "fast" to topology changes. If s (n) is an upper bound on the convergence time and d (n) is an upper bound on the convergence time following a topology change, then s (n) ∈ o (n) and d (n) ∈ o (s (n)). The self-organization property can then be used for gaining, in sub-linear time, global properties and reaction to changes. We present self-stabilizing and self-organizing algorithms for many distributed algorithms, including distributed snapshot and leader election. We present a new randomized self-stabilizing distributed algorithm for cluster definition in communication graphs of bounded degree processors. These graphs reflect sensor networks deployment. The algorithm converges in O (log n) expected number of rounds, handles dynamic changes locally and is, therefore, self-organizing. Applying the clustering algorithm to specific classes of communication graphs, in O (log n) levels, using an overlay network abstraction, results in a self-stabilizing and self-organizing distributed algorithm for hierarchy definition. Given the obtained hierarchy definition, we present an algorithm for hierarchical distributed snapshots. The algorithms are based on a new basic snap-stabilizing snapshot algorithm, designed for message passing systems in which a distributed spanning tree is defined and in which processors communicate using bounded links capacity. The algorithm is on-demand self-stabilizing when no such distributed spanning tree is defined. Namely, it stabilizes regardless of the number of snapshot invocations. The combination of the self-stabilizing and self-organizing distributed hierarchy construction and the snapshot algorithm forms an efficient self-stabilizer transformer. Given a distributed algorithm for a specific task, we are able to convert the algorithm into a self-stabilizing algorithm for the same task with an expected convergence time of O (log^{2} n) rounds.

Original language | English |
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Pages (from-to) | 514-532 |

Number of pages | 19 |

Journal | Theoretical Computer Science |

Volume | 410 |

Issue number | 6-7 |

DOIs | |

State | Published - 28 Feb 2009 |

## Keywords

- Clustering
- Communication and routing
- Self-organizing
- Self-stabilizing

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science