681 research outputs found
Iterative Approximate Consensus in the presence of Byzantine Link Failures
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each directed link of the underlying
communication graph represents a communication channel between a pair of nodes.
We adopt the transient Byzantine link failure model [15, 16], where an
omniscient adversary controls a subset of the directed communication links, but
the nodes are assumed to be fault-free.
Recent work has addressed the problem of reaching approximate consen- sus in
incomplete graphs with Byzantine nodes using a restricted class of iterative
algorithms that maintain only a small amount of memory across iterations [22,
21, 23, 12]. However, to the best of our knowledge, we are the first to
consider approximate consensus in the presence of Byzan- tine links. We extend
our past work that provided exact characterization of graphs in which the
iterative approximate consensus problem in the presence of Byzantine node
failures is solvable [22, 21]. In particular, we prove a tight necessary and
sufficient condition on the underlying com- munication graph for the existence
of iterative approximate consensus algorithms under transient Byzantine link
model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609
An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each pair of nodes is able to
communicate with each other directly and reliably. We consider the mobile
Byzantine fault model proposed by Garay '94 -- in the model, an omniscient
adversary can corrupt up to nodes in each round, and at the beginning of
each round, faults may "move" in the system (i.e., different sets of nodes may
become faulty in different rounds). Recent work by Bonomi et al. '16 proposed a
simple iterative approximate consensus algorithm which requires at least
nodes. This paper proposes a novel technique of using "confession" (a mechanism
to allow others to ignore past behavior) and a variant of reliable broadcast to
improve the fault-tolerance level. In particular, we present an approximate
consensus algorithm that requires only nodes, an
improvement over the state-of-the-art algorithms.
Moreover, we also show that the proposed algorithm is optimal within a family
of round-based algorithms
Reliable Communication in a Dynamic Network in the Presence of Byzantine Faults
We consider the following problem: two nodes want to reliably communicate in
a dynamic multihop network where some nodes have been compromised, and may have
a totally arbitrary and unpredictable behavior. These nodes are called
Byzantine. We consider the two cases where cryptography is available and not
available. We prove the necessary and sufficient condition (that is, the
weakest possible condition) to ensure reliable communication in this context.
Our proof is constructive, as we provide Byzantine-resilient algorithms for
reliable communication that are optimal with respect to our impossibility
results. In a second part, we investigate the impact of our conditions in three
case studies: participants interacting in a conference, robots moving on a grid
and agents in the subway. Our simulations indicate a clear benefit of using our
algorithms for reliable communication in those contexts
Reaching Approximate Byzantine Consensus in Partially-Connected Mobile Networks
We consider the problem of approximate consensus in mobile networks
containing Byzantine nodes. We assume that each correct node can communicate
only with its neighbors and has no knowledge of the global topology. As all
nodes have moving ability, the topology is dynamic. The number of Byzantine
nodes is bounded by f and known by all correct nodes. We first introduce an
approximate Byzantine consensus protocol which is based on the linear iteration
method. As nodes are allowed to collect information during several consecutive
rounds, moving gives them the opportunity to gather more values. We propose a
novel sufficient and necessary condition to guarantee the final convergence of
the consensus protocol. The requirement expressed by our condition is not
"universal": in each phase it affects only a single correct node. More
precisely, at least one correct node among those that propose either the
minimum or the maximum value which is present in the network, has to receive
enough messages (quantity constraint) with either higher or lower values
(quality constraint). Of course, nodes' motion should not prevent this
requirement to be fulfilled. Our conclusion shows that the proposed condition
can be satisfied if the total number of nodes is greater than 3f+1.Comment: No. RR-7985 (2012
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