3,288 research outputs found
Message-Passing Algorithms for Quadratic Minimization
Gaussian belief propagation (GaBP) is an iterative algorithm for computing
the mean of a multivariate Gaussian distribution, or equivalently, the minimum
of a multivariate positive definite quadratic function. Sufficient conditions,
such as walk-summability, that guarantee the convergence and correctness of
GaBP are known, but GaBP may fail to converge to the correct solution given an
arbitrary positive definite quadratic function. As was observed in previous
work, the GaBP algorithm fails to converge if the computation trees produced by
the algorithm are not positive definite. In this work, we will show that the
failure modes of the GaBP algorithm can be understood via graph covers, and we
prove that a parameterized generalization of the min-sum algorithm can be used
to ensure that the computation trees remain positive definite whenever the
input matrix is positive definite. We demonstrate that the resulting algorithm
is closely related to other iterative schemes for quadratic minimization such
as the Gauss-Seidel and Jacobi algorithms. Finally, we observe, empirically,
that there always exists a choice of parameters such that the above
generalization of the GaBP algorithm converges
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
The role of concurrency in an evolutionary view of programming abstractions
In this paper we examine how concurrency has been embodied in mainstream
programming languages. In particular, we rely on the evolutionary talking
borrowed from biology to discuss major historical landmarks and crucial
concepts that shaped the development of programming languages. We examine the
general development process, occasionally deepening into some language, trying
to uncover evolutionary lineages related to specific programming traits. We
mainly focus on concurrency, discussing the different abstraction levels
involved in present-day concurrent programming and emphasizing the fact that
they correspond to different levels of explanation. We then comment on the role
of theoretical research on the quest for suitable programming abstractions,
recalling the importance of changing the working framework and the way of
looking every so often. This paper is not meant to be a survey of modern
mainstream programming languages: it would be very incomplete in that sense. It
aims instead at pointing out a number of remarks and connect them under an
evolutionary perspective, in order to grasp a unifying, but not simplistic,
view of the programming languages development process
Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems
In this paper, we show that the protocol complex of a Byzantine synchronous
system can remain -connected for up to rounds,
where is the maximum number of Byzantine processes, and .
This topological property implies that rounds are
necessary to solve -set agreement in Byzantine synchronous systems, compared
to rounds in synchronous crash-failure systems. We
also show that our connectivity bound is tight as we indicate solutions to
Byzantine -set agreement in exactly synchronous
rounds, at least when is suitably large compared to . In conclusion, we
see how Byzantine failures can potentially require one extra round to solve
-set agreement, and, for suitably large compared to , at most that
Actors vs Shared Memory: two models at work on Big Data application frameworks
This work aims at analyzing how two different concurrency models, namely the
shared memory model and the actor model, can influence the development of
applications that manage huge masses of data, distinctive of Big Data
applications. The paper compares the two models by analyzing a couple of
concrete projects based on the MapReduce and Bulk Synchronous Parallel
algorithmic schemes. Both projects are doubly implemented on two concrete
platforms: Akka Cluster and Managed X10. The result is both a conceptual
comparison of models in the Big Data Analytics scenario, and an experimental
analysis based on concrete executions on a cluster platform
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