114 research outputs found
Bounding the Impact of Unbounded Attacks in Stabilization
Self-stabilization is a versatile approach to fault-tolerance since it
permits a distributed system to recover from any transient fault that
arbitrarily corrupts the contents of all memories in the system. Byzantine
tolerance is an attractive feature of distributed systems that permits to cope
with arbitrary malicious behaviors. Combining these two properties proved
difficult: it is impossible to contain the spatial impact of Byzantine nodes in
a self-stabilizing context for global tasks such as tree orientation and tree
construction. We present and illustrate a new concept of Byzantine containment
in stabilization. Our property, called Strong Stabilization enables to contain
the impact of Byzantine nodes if they actually perform too many Byzantine
actions. We derive impossibility results for strong stabilization and present
strongly stabilizing protocols for tree orientation and tree construction that
are optimal with respect to the number of Byzantine nodes that can be tolerated
in a self-stabilizing context
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
Self-Stabilization, Byzantine Containment, and Maximizable Metrics: Necessary Conditions
Self-stabilization is a versatile approach to fault-tolerance since it
permits a distributed system to recover from any transient fault that
arbitrarily corrupts the contents of all memories in the system. Byzantine
tolerance is an attractive feature of distributed systems that permits to cope
with arbitrary malicious behaviors. We consider the well known problem of
constructing a maximum metric tree in this context. Combining these two
properties leads to some impossibility results. In this paper, we provide two
necessary conditions to construct maximum metric tree in presence of transients
and (permanent) Byzantine faults
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
Quiescence of Self-stabilizing Gossiping among Mobile Agents in Graphs
This paper considers gossiping among mobile agents in graphs: agents move on
the graph and have to disseminate their initial information to every other
agent. We focus on self-stabilizing solutions for the gossip problem, where
agents may start from arbitrary locations in arbitrary states.
Self-stabilization requires (some of the) participating agents to keep moving
forever, hinting at maximizing the number of agents that could be allowed to
stop moving eventually. This paper formalizes the self-stabilizing agent gossip
problem, introduces the quiescence number (i.e., the maximum number of
eventually stopping agents) of self-stabilizing solutions and investigates the
quiescence number with respect to several assumptions related to agent
anonymity, synchrony, link duplex capacity, and whiteboard capacity
Self-Stabilizing Token Distribution with Constant-Space for Trees
Self-stabilizing and silent distributed algorithms for token distribution in rooted tree networks are given. Initially, each process of a graph holds at most l tokens. Our goal is to distribute the tokens in the whole network so that every process holds exactly k tokens. In the initial configuration, the total number of tokens in the network may not be equal to nk where n is the number of processes in the network. The root process is given the ability to create a new token or remove a token from the network. We aim to minimize the convergence time, the number of token moves, and the space complexity. A self-stabilizing token distribution algorithm that converges within O(n l) asynchronous rounds and needs Theta(nh epsilon) redundant (or unnecessary) token moves is given, where epsilon = min(k,l-k) and h is the height of the tree network. Two novel ideas to reduce the number of redundant token moves are presented. One reduces the number of redundant token moves to O(nh) without any additional costs while the other reduces the number of redundant token moves to O(n), but increases the convergence time to O(nh l). All algorithms given have constant memory at each process and each link register
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