14,746 research outputs found
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
Silent MST approximation for tiny memory
In network distributed computing, minimum spanning tree (MST) is one of the
key problems, and silent self-stabilization one of the most demanding
fault-tolerance properties. For this problem and this model, a polynomial-time
algorithm with memory is known for the state model. This is
memory optimal for weights in the classic range (where
is the size of the network). In this paper, we go below this
memory, using approximation and parametrized complexity.
More specifically, our contributions are two-fold. We introduce a second
parameter~, which is the space needed to encode a weight, and we design a
silent polynomial-time self-stabilizing algorithm, with space . In turn, this allows us to get an approximation algorithm for the problem,
with a trade-off between the approximation ratio of the solution and the space
used. For polynomial weights, this trade-off goes smoothly from memory for an -approximation, to memory for exact solutions,
with for example memory for a 2-approximation
Fast Consensus under Eventually Stabilizing Message Adversaries
This paper is devoted to deterministic consensus in synchronous dynamic
networks with unidirectional links, which are under the control of an
omniscient message adversary. Motivated by unpredictable node/system
initialization times and long-lasting periods of massive transient faults, we
consider message adversaries that guarantee periods of less erratic message
loss only eventually: We present a tight bound of for the termination
time of consensus under a message adversary that eventually guarantees a single
vertex-stable root component with dynamic network diameter , as well as a
simple algorithm that matches this bound. It effectively halves the termination
time achieved by an existing consensus algorithm, which also works under
our message adversary. We also introduce a generalized, considerably stronger
variant of our message adversary, and show that our new algorithm, unlike the
existing one, still works correctly under it.Comment: 13 pages, 5 figures, updated reference
Fast and compact self-stabilizing verification, computation, and fault detection of an MST
This paper demonstrates the usefulness of distributed local verification of
proofs, as a tool for the design of self-stabilizing algorithms.In particular,
it introduces a somewhat generalized notion of distributed local proofs, and
utilizes it for improving the time complexity significantly, while maintaining
space optimality. As a result, we show that optimizing the memory size carries
at most a small cost in terms of time, in the context of Minimum Spanning Tree
(MST). That is, we present algorithms that are both time and space efficient
for both constructing an MST and for verifying it.This involves several parts
that may be considered contributions in themselves.First, we generalize the
notion of local proofs, trading off the time complexity for memory efficiency.
This adds a dimension to the study of distributed local proofs, which has been
gaining attention recently. Specifically, we design a (self-stabilizing) proof
labeling scheme which is memory optimal (i.e., bits per node), and
whose time complexity is in synchronous networks, or time in asynchronous ones, where is the maximum degree of
nodes. This answers an open problem posed by Awerbuch and Varghese (FOCS 1991).
We also show that time is necessary, even in synchronous
networks. Another property is that if faults occurred, then, within the
requireddetection time above, they are detected by some node in the locality of each of the faults.Second, we show how to enhance a known
transformer that makes input/output algorithms self-stabilizing. It now takes
as input an efficient construction algorithm and an efficient self-stabilizing
proof labeling scheme, and produces an efficient self-stabilizing algorithm.
When used for MST, the transformer produces a memory optimal self-stabilizing
algorithm, whose time complexity, namely, , is significantly better even
than that of previous algorithms. (The time complexity of previous MST
algorithms that used memory bits per node was , and
the time for optimal space algorithms was .) Inherited from our proof
labelling scheme, our self-stabilising MST construction algorithm also has the
following two properties: (1) if faults occur after the construction ended,
then they are detected by some nodes within time in synchronous
networks, or within time in asynchronous ones, and (2) if
faults occurred, then, within the required detection time above, they are
detected within the locality of each of the faults. We also show
how to improve the above two properties, at the expense of some increase in the
memory
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