496 research outputs found
Iterative Approximate Byzantine Consensus under a Generalized Fault Model
In this work, we consider a generalized fault model that can be used to
represent a wide range of failure scenarios, including correlated failures and
non-uniform node reliabilities. This fault model is general in the sense that
fault models studied in prior related work, such as f -total and f -local
models, are special cases of the generalized fault model. Under the generalized
fault model, we explore iterative approximate Byzantine consensus (IABC)
algorithms in arbitrary directed networks. We prove a necessary and sufficient
condition for the existence of IABC algorithms. The use of the generalized
fault model helps to gain a better understanding of IABC algorithms.Comment: arXiv admin note: text overlap with arXiv:1203.188
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
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
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