2,241 research outputs found
Bounds for self-stabilization in unidirectional networks
A distributed algorithm is self-stabilizing if after faults and attacks hit
the system and place it in some arbitrary global state, the systems recovers
from this catastrophic situation without external intervention in finite time.
Unidirectional networks preclude many common techniques in self-stabilization
from being used, such as preserving local predicates. In this paper, we
investigate the intrinsic complexity of achieving self-stabilization in
unidirectional networks, and focus on the classical vertex coloring problem.
When deterministic solutions are considered, we prove a lower bound of
states per process (where is the network size) and a recovery time of at
least actions in total. We present a deterministic algorithm with
matching upper bounds that performs in arbitrary graphs. When probabilistic
solutions are considered, we observe that at least states per
process and a recovery time of actions in total are required (where
denotes the maximal degree of the underlying simple undirected graph).
We present a probabilistically self-stabilizing algorithm that uses
states per process, where is a parameter of the
algorithm. When , the algorithm recovers in expected
actions. When may grow arbitrarily, the algorithm
recovers in expected O(n) actions in total. Thus, our algorithm can be made
optimal with respect to space or time complexity
Separation of Circulating Tokens
Self-stabilizing distributed control is often modeled by token abstractions.
A system with a single token may implement mutual exclusion; a system with
multiple tokens may ensure that immediate neighbors do not simultaneously enjoy
a privilege. For a cyber-physical system, tokens may represent physical objects
whose movement is controlled. The problem studied in this paper is to ensure
that a synchronous system with m circulating tokens has at least d distance
between tokens. This problem is first considered in a ring where d is given
whilst m and the ring size n are unknown. The protocol solving this problem can
be uniform, with all processes running the same program, or it can be
non-uniform, with some processes acting only as token relays. The protocol for
this first problem is simple, and can be expressed with Petri net formalism. A
second problem is to maximize d when m is given, and n is unknown. For the
second problem, the paper presents a non-uniform protocol with a single
corrective process.Comment: 22 pages, 7 figures, epsf and pstricks in LaTe
Automated Synthesis of Distributed Self-Stabilizing Protocols
In this paper, we introduce an SMT-based method that automatically
synthesizes a distributed self-stabilizing protocol from a given high-level
specification and network topology. Unlike existing approaches, where synthesis
algorithms require the explicit description of the set of legitimate states,
our technique only needs the temporal behavior of the protocol. We extend our
approach to synthesize ideal-stabilizing protocols, where every state is
legitimate. We also extend our technique to synthesize monotonic-stabilizing
protocols, where during recovery, each process can execute an most once one
action. Our proposed methods are fully implemented and we report successful
synthesis of well-known protocols such as Dijkstra's token ring, a
self-stabilizing version of Raymond's mutual exclusion algorithm,
ideal-stabilizing leader election and local mutual exclusion, as well as
monotonic-stabilizing maximal independent set and distributed Grundy coloring
Stabilizing Maximal Independent Set in Unidirectional Networks is Hard
A distributed algorithm is self-stabilizing if after faults and attacks hit
the system and place it in some arbitrary global state, the system recovers
from this catastrophic situation without external intervention in finite time.
In this paper, we consider the problem of constructing self-stabilizingly a
\emph{maximal independent set} in uniform unidirectional networks of arbitrary
shape. On the negative side, we present evidence that in uniform networks,
\emph{deterministic} self-stabilization of this problem is \emph{impossible}.
Also, the \emph{silence} property (\emph{i.e.} having communication fixed from
some point in every execution) is impossible to guarantee, either for
deterministic or for probabilistic variants of protocols. On the positive side,
we present a deterministic protocol for networks with arbitrary unidirectional
networks with unique identifiers that exhibits polynomial space and time
complexity in asynchronous scheduling. We complement the study with
probabilistic protocols for the uniform case: the first probabilistic protocol
requires infinite memory but copes with asynchronous scheduling, while the
second probabilistic protocol has polynomial space complexity but can only
handle synchronous scheduling. Both probabilistic solutions have expected
polynomial time complexity
Enhancement of synchronization in a hybrid neural circuit by spike timing dependent plasticity
Synchronization of neural activity is fundamental for many functions of the brain. We demonstrate that spike-timing dependent plasticity (STDP) enhances synchronization (entrainment) in a hybrid circuit composed of a spike generator, a dynamic clamp emulating an excitatory plastic synapse, and a chemically isolated neuron from the Aplysia abdominal ganglion. Fixed-phase entrainment of the Aplysia neuron to the spike generator is possible for a much wider range of frequency ratios and is more precise and more robust with the plastic synapse than with a nonplastic synapse of comparable strength. Further analysis in a computational model of HodgkinHuxley-type neurons reveals the mechanism behind this significant enhancement in synchronization. The experimentally observed STDP plasticity curve appears to be designed to adjust synaptic strength to a value suitable for stable entrainment of the postsynaptic neuron. One functional role of STDP might therefore be to facilitate synchronization or entrainment of nonidentical neurons
Compact Deterministic Self-Stabilizing Leader Election: The Exponential Advantage of Being Talkative
This paper focuses on compact deterministic self-stabilizing solutions for
the leader election problem. When the protocol is required to be \emph{silent}
(i.e., when communication content remains fixed from some point in time during
any execution), there exists a lower bound of Omega(\log n) bits of memory per
node participating to the leader election (where n denotes the number of nodes
in the system). This lower bound holds even in rings. We present a new
deterministic (non-silent) self-stabilizing protocol for n-node rings that uses
only O(\log\log n) memory bits per node, and stabilizes in O(n\log^2 n) rounds.
Our protocol has several attractive features that make it suitable for
practical purposes. First, the communication model fits with the model used by
existing compilers for real networks. Second, the size of the ring (or any
upper bound on this size) needs not to be known by any node. Third, the node
identifiers can be of various sizes. Finally, no synchrony assumption, besides
a weakly fair scheduler, is assumed. Therefore, our result shows that, perhaps
surprisingly, trading silence for exponential improvement in term of memory
space does not come at a high cost regarding stabilization time or minimal
assumptions
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
A Lightweight, Non-intrusive Approach for Orchestrating Autonomously-managed Network Elements
Software-Defined Networking enables the centralized orchestration of data
traffic within a network. However, proposed solutions require a high degree of
architectural penetration. The present study targets the orchestration of
network elements that do not wish to yield much of their internal operations to
an external controller. Backpressure routing principles are used for deriving
flow routing rules that optimally stabilize a network, while maximizing its
throughput. The elements can then accept in full, partially or reject the
proposed routing rule-set. The proposed scheme requires minimal, relatively
infrequent interaction with a controller, limiting its imposed workload,
promoting scalability. The proposed scheme exhibits attracting network
performance gains, as demonstrated by extensive simulations and proven via
mathematical analysis.Comment: 6 pages 7, figures, IEEE ISCC'1
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