1,270 research outputs found
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
Optimal byzantine resilient convergence in oblivious robot networks
Given a set of robots with arbitrary initial location and no agreement on a
global coordinate system, convergence requires that all robots asymptotically
approach the exact same, but unknown beforehand, location. Robots are
oblivious-- they do not recall the past computations -- and are allowed to move
in a one-dimensional space. Additionally, robots cannot communicate directly,
instead they obtain system related information only via visual sensors. We draw
a connection between the convergence problem in robot networks, and the
distributed \emph{approximate agreement} problem (that requires correct
processes to decide, for some constant , values distance
apart and within the range of initial proposed values). Surprisingly, even
though specifications are similar, the convergence implementation in robot
networks requires specific assumptions about synchrony and Byzantine
resilience. In more details, we prove necessary and sufficient conditions for
the convergence of mobile robots despite a subset of them being Byzantine (i.e.
they can exhibit arbitrary behavior). Additionally, we propose a deterministic
convergence algorithm for robot networks and analyze its correctness and
complexity in various synchrony settings. The proposed algorithm tolerates f
Byzantine robots for (2f+1)-sized robot networks in fully synchronous networks,
(3f+1)-sized in semi-synchronous networks. These bounds are optimal for the
class of cautious algorithms, which guarantee that correct robots always move
inside the range of positions of the correct robots
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
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
Asynchronous Convex Consensus in the Presence of Crash Faults
This paper defines a new consensus problem, convex consensus. Similar to
vector consensus [13, 20, 19], the input at each process is a d-dimensional
vector of reals (or, equivalently, a point in the d-dimensional Euclidean
space). However, for convex consensus, the output at each process is a convex
polytope contained within the convex hull of the inputs at the fault-free
processes. We explore the convex consensus problem under crash faults with
incorrect inputs, and present an asynchronous approximate convex consensus
algorithm with optimal fault tolerance that reaches consensus on an optimal
output polytope. Convex consensus can be used to solve other related problems.
For instance, a solution for convex consensus trivially yields a solution for
vector consensus. More importantly, convex consensus can potentially be used to
solve other more interesting problems, such as convex function optimization [5,
4].Comment: A version of this work is published in PODC 201
Consensus of Multi-Agent Networks in the Presence of Adversaries Using Only Local Information
This paper addresses the problem of resilient consensus in the presence of
misbehaving nodes. Although it is typical to assume knowledge of at least some
nonlocal information when studying secure and fault-tolerant consensus
algorithms, this assumption is not suitable for large-scale dynamic networks.
To remedy this, we emphasize the use of local strategies to deal with
resilience to security breaches. We study a consensus protocol that uses only
local information and we consider worst-case security breaches, where the
compromised nodes have full knowledge of the network and the intentions of the
other nodes. We provide necessary and sufficient conditions for the normal
nodes to reach consensus despite the influence of the malicious nodes under
different threat assumptions. These conditions are stated in terms of a novel
graph-theoretic property referred to as network robustness.Comment: This report contains the proofs of the results presented at HiCoNS
201
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
Matrix Representation of Iterative Approximate Byzantine Consensus in Directed Graphs
This paper presents a proof of correctness of an iterative approximate
Byzantine consensus (IABC) algorithm for directed graphs. The iterative
algorithm allows fault- free nodes to reach approximate conensus despite the
presence of up to f Byzantine faults. Necessary conditions on the underlying
network graph for the existence of a correct IABC algorithm were shown in our
recent work [15, 16]. [15] also analyzed a specific IABC algorithm and showed
that it performs correctly in any network graph that satisfies the necessary
condition, proving that the necessary condition is also sufficient. In this
paper, we present an alternate proof of correctness of the IABC algorithm,
using a familiar technique based on transition matrices [9, 3, 17, 19].
The key contribution of this paper is to exploit the following observation:
for a given evolution of the state vector corresponding to the state of the
fault-free nodes, many alternate state transition matrices may be chosen to
model that evolution cor- rectly. For a given state evolution, we identify one
approach to suitably "design" the transition matrices so that the standard
tools for proving convergence can be applied to the Byzantine fault-tolerant
algorithm as well. In particular, the transition matrix for each iteration is
designed such that each row of the matrix contains a large enough number of
elements that are bounded away from 0
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