916 research outputs found
The Contest Between Simplicity and Efficiency in Asynchronous Byzantine Agreement
In the wake of the decisive impossibility result of Fischer, Lynch, and
Paterson for deterministic consensus protocols in the aynchronous model with
just one failure, Ben-Or and Bracha demonstrated that the problem could be
solved with randomness, even for Byzantine failures. Both protocols are natural
and intuitive to verify, and Bracha's achieves optimal resilience. However, the
expected running time of these protocols is exponential in general. Recently,
Kapron, Kempe, King, Saia, and Sanwalani presented the first efficient
Byzantine agreement algorithm in the asynchronous, full information model,
running in polylogarithmic time. Their algorithm is Monte Carlo and drastically
departs from the simple structure of Ben-Or and Bracha's Las Vegas algorithms.
In this paper, we begin an investigation of the question: to what extent is
this departure necessary? Might there be a much simpler and intuitive Las Vegas
protocol that runs in expected polynomial time? We will show that the
exponential running time of Ben-Or and Bracha's algorithms is no mere accident
of their specific details, but rather an unavoidable consequence of their
general symmetry and round structure. We define a natural class of "fully
symmetric round protocols" for solving Byzantine agreement in an asynchronous
setting and show that any such protocol can be forced to run in expected
exponential time by an adversary in the full information model. We assume the
adversary controls Byzantine processors for , where is an
arbitrary positive constant . We view our result as a step toward
identifying the level of complexity required for a polynomial-time algorithm in
this setting, and also as a guide in the search for new efficient algorithms.Comment: 21 page
Byzantine Approximate Agreement on Graphs
Consider a distributed system with n processors out of which f can be Byzantine faulty. In the approximate agreement task, each processor i receives an input value x_i and has to decide on an output value y_i such that
1) the output values are in the convex hull of the non-faulty processors\u27 input values,
2) the output values are within distance d of each other.
Classically, the values are assumed to be from an m-dimensional Euclidean space, where m >= 1.
In this work, we study the task in a discrete setting, where input values with some structure expressible as a graph. Namely, the input values are vertices of a finite graph G and the goal is to output vertices that are within distance d of each other in G, but still remain in the graph-induced convex hull of the input values. For d=0, the task reduces to consensus and cannot be solved with a deterministic algorithm in an asynchronous system even with a single crash fault. For any d >= 1, we show that the task is solvable in asynchronous systems when G is chordal and n > (omega+1)f, where omega is the clique number of G. In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures
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