146 research outputs found
Avatar: A Time- and Space-Efficient Self-Stabilizing Overlay Network
Overlay networks present an interesting challenge for fault-tolerant
computing. Many overlay networks operate in dynamic environments (e.g. the
Internet), where faults are frequent and widespread, and the number of
processes in a system may be quite large. Recently, self-stabilizing overlay
networks have been presented as a method for managing this complexity.
\emph{Self-stabilizing overlay networks} promise that, starting from any
weakly-connected configuration, a correct overlay network will eventually be
built. To date, this guarantee has come at a cost: nodes may either have high
degree during the algorithm's execution, or the algorithm may take a long time
to reach a legal configuration. In this paper, we present the first
self-stabilizing overlay network algorithm that does not incur this penalty.
Specifically, we (i) present a new locally-checkable overlay network based upon
a binary search tree, and (ii) provide a randomized algorithm for
self-stabilization that terminates in an expected polylogarithmic number of
rounds \emph{and} increases a node's degree by only a polylogarithmic factor in
expectation
Self-Stabilizing Supervised Publish-Subscribe Systems
In this paper we present two major results: First, we introduce the first
self-stabilizing version of a supervised overlay network by presenting a
self-stabilizing supervised skip ring. Secondly, we show how to use the
self-stabilizing supervised skip ring to construct an efficient
self-stabilizing publish-subscribe system. That is, in addition to stabilizing
the overlay network, every subscriber of a topic will eventually know all of
the publications that have been issued so far for that topic. The communication
work needed to processes a subscribe or unsubscribe operation is just a
constant in a legitimate state, and the communication work of checking whether
the system is still in a legitimate state is just a constant on expectation for
the supervisor as well as any process in the system
HSkip+: A Self-Stabilizing Overlay Network for Nodes with Heterogeneous Bandwidths
In this paper we present and analyze HSkip+, a self-stabilizing overlay
network for nodes with arbitrary heterogeneous bandwidths. HSkip+ has the same
topology as the Skip+ graph proposed by Jacob et al. [PODC 2009] but its
self-stabilization mechanism significantly outperforms the self-stabilization
mechanism proposed for Skip+. Also, the nodes are now ordered according to
their bandwidths and not according to their identifiers. Various other
solutions have already been proposed for overlay networks with heterogeneous
bandwidths, but they are not self-stabilizing. In addition to HSkip+ being
self-stabilizing, its performance is on par with the best previous bounds on
the time and work for joining or leaving a network of peers of logarithmic
diameter and degree and arbitrary bandwidths. Also, the dilation and congestion
for routing messages is on par with the best previous bounds for such networks,
so that HSkip+ combines the advantages of both worlds. Our theoretical
investigations are backed by simulations demonstrating that HSkip+ is indeed
performing much better than Skip+ and working correctly under high churn rates.Comment: This is a long version of a paper published by IEEE in the
Proceedings of the 14-th IEEE International Conference on Peer-to-Peer
Computin
Towards Establishing Monotonic Searchability in Self-Stabilizing Data Structures
Distributed applications are commonly based on overlay networks interconnecting their sites so that they can exchange information. For these overlay networks to preserve their functionality, they should be able to recover from various problems like membership changes or faults. Various self-stabilizing overlay networks have already been proposed in recent years, which have the advantage of being able to recover from any illegal state, but none of these networks can give any guarantees on its functionality while the recovery process is going on. We initiate research on overlay networks that are not only self-stabilizing but that also ensure that searchability is maintained while the recovery process is going on, as long as there are no corrupted messages in the system. More precisely, once a search message from node u to another node v is successfully delivered, all future search messages from u to v succeed as well. We call this property monotonic searchability. We show that in general it is impossible to provide monotonic searchability if corrupted messages are present in the system, which justifies the restriction to system states without corrupted messages. Furthermore, we provide a self-stabilizing protocol for the line for which we can also show monotonic searchability. It turns out that even for the line it is non-trivial to achieve this property. Additionally, we extend our protocol to deal with node departures in terms of the Finite Departure Problem of Foreback et al. (SSS 2014). This makes our protocol even capable of handling node dynamics
Self-stabilizing Overlays for high-dimensional Monotonic Searchability
We extend the concept of monotonic searchability for self-stabilizing systems
from one to multiple dimensions. A system is self-stabilizing if it can recover
to a legitimate state from any initial illegal state. These kind of systems are
most often used in distributed applications. Monotonic searchability provides
guarantees when searching for nodes while the recovery process is going on.
More precisely, if a search request started at some node succeeds in
reaching its destination , then all future search requests from to
succeed as well. Although there already exists a self-stabilizing protocol for
a two-dimensional topology and an universal approach for monotonic
searchability, it is not clear how both of these concepts fit together
effectively. The latter concept even comes with some restrictive assumptions on
messages, which is not the case for our protocol. We propose a simple novel
protocol for a self-stabilizing two-dimensional quadtree that satisfies
monotonic searchability. Our protocol can easily be extended to higher
dimensions and offers routing in hops for any search
request
On the Complexity of Local Graph Transformations
We consider the problem of transforming a given graph G_s into a desired graph G_t by applying a minimum number of primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each node can apply them based on local knowledge and by affecting only its 1-neighborhood. Although the specific set of primitives we consider makes it possible to transform any (weakly) connected graph into any other (weakly) connected graph consisting of the same nodes, they cannot disconnect the graph or introduce new nodes into the graph, making them ideal in the context of supervised overlay network transformations. We prove that computing a minimum sequence of primitive applications (even centralized) for arbitrary G_s and G_t is NP-hard, which we conjecture to hold for any set of local graph transformation primitives satisfying the aforementioned properties. On the other hand, we show that this problem admits a polynomial time algorithm with a constant approximation ratio
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