Fault-Local Distributed Mending

Abstract

As communication networks grow, existing fault handling tools that involve global measures such as global time-outs or reset procedures become increasingly unaffordable, since their cost grows with the size of the network. Rather, for a fault handling mechanism to scale to large networks, its cost must depend only on the Ž number of failed nodes which, thanks to today's technology, grows much more . slowly than the networks . Moreover, it should allow the nonfaulty regions of the networks to continue their operation even during the recovery of the faulty parts. This paper introduces the concepts fault locality and fault-locally mendable prob-Ž lems, which are problems for which there are correction algorithms applied after . Ž . faults whose cost depends only on the unknown number of faults. We show that any input-output problem is fault-locally mendable. The solution involves a novel technique combining data structures and ''local votes'' among nodes, which may be of interest in itself.

Adaptive Stabilization of Reactive Protocols

“…As a corollary, the presented protocol shows that theoretically, any reactive task admits a self-stabilizing adaptive implementation. Our protocol complements results of [22,21] dealing with non-reactive tasks. There, it is assumed that all inputs and outputs are initially replicated at all nodes.…”

“…Intuitively, the reason for that is that reset-based stabilization is too "twitchy": the slightest disturbance to the consistency of the system may trigger a systemwide service outage (or "hiccup") for a non-negligible amount of time, which is clearly undesirable. In response to this shortcoming, a new approach, called adaptive protocols, has recently taken the focus of attention in this research area [23,18,22,21,3]. Informally, a stabilizing system is called adaptive if its recovery time depends on the severity of the fault, measured by the number of processors whose state was corrupted.…”

“…The idea of adaptive protocols (with variants called fault-local, local stabilizing, or fault containing) is treated in [22,23,18,21,6,7], all of them non-reactive.…”

Necessary and sufficient conditions for 1-adaptivity

“…The first time adaptive algorithms, as well as the notion of fault locality, where both presented in [18] and [15]. They were introduced in the context of non reactive problems.…”

Peer-to-Peer Data Mining, Privacy Issues, and Games

“…For more scalable approaches, researchers explored the paradigm of local algorithms for doing data mining in P2P network. Local algorithms [12,16,2,11,10] are ones in which the result is usually computed using information from just a handful of nearby neighbors. Still, it is possible to make definite claims about the correctness of the result.…”