Consider an asynchronous network in a shared-memory environment consisting of
n nodes. Assume that up to f of the nodes might be Byzantine (n > 12f), where
the adversary is full-information and dynamic (sometimes called adaptive). In
addition, the non-Byzantine nodes may undergo transient failures. Nodes advance
in atomic steps, which consist of reading all registers, performing some
calculation and writing to all registers.
Gradecast is a simple three-round algorithm presented by Feldman and Micali.
The current work presents a very simple algorithm that utilized Gradecast to
achieve Byzantine agreement. Two small variations of the presented algorithm
lead to improved algorithms for solving the Approximate agreement problem and
the Multi-consensus problem.
An optimal approximate agreement algorithm was presented by Fekete, which
supports up to 1/4 n Byzantine nodes and has message complexity of O(n^k),
where n is the number of nodes and k is the number of rounds.
We propose a new distributed algorithm for computing a truncated Newton
method, where the main diagonal of the Hessian is computed using belief
propagation. As a case study for this approach, we examine the sensor selection
problem, a Boolean convex optimization problem. We form two distributed
algorithms. The first algorithm is a distributed version of the interior point
method by Joshi and Boyd, and the second algorithm is an order of magnitude
faster approximation. As an example application we discuss distributed anomaly
detection in networks.
We consider the problem of estimating a pattern of faults, represented as a
binary vector, from a set of measurements. Maximum a posteriori probability
(MAP) estimation of the fault pattern leads to a difficult combinatorial
optimization problem. Following recent success of the belief propagation
framework in the related compressive sensing and low density lattice decoding
domains, we propose a novel relaxation of the problem using non-parametric
belief propagation (NBP) for creating a distributed solution.