11,647 research outputs found
Lattice Agreement in Message Passing Systems
This paper studies the lattice agreement problem and the generalized lattice agreement problem in distributed message passing systems. In the lattice agreement problem, given input values from a lattice, processes have to non-trivially decide output values that lie on a chain. We consider the lattice agreement problem in both synchronous and asynchronous systems. For synchronous lattice agreement, we present two algorithms which run in log(f) and min{O(log^2 h(L)), O(log^2 f)} rounds, respectively, where h(L) denotes the height of the input sublattice L, f < n is the number of crash failures the system can tolerate, and n is the number of processes in the system. These algorithms have significant better round complexity than previously known algorithms. The algorithm by Attiya et al. [Attiya et al. DISC, 1995] takes log(n) synchronous rounds, and the algorithm by Mavronicolasa [Mavronicolasa, 2018] takes min{O(h(L)), O(sqrt(f))} rounds. For asynchronous lattice agreement, we propose an algorithm which has time complexity of 2*min{h(L), f + 1} message delays which improves on the previously known time complexity of O(n) message delays.
The generalized lattice agreement problem defined by Faleiro et al in [Faleiro et al. PODC, 2012] is a generalization of the lattice agreement problem where it is applied for the replicated state machine. We propose an algorithm which guarantees liveness when a majority of the processes are correct in asynchronous systems. Our algorithm requires min{O(h(L)), O(f)} units of time in the worst case which is better than O(n) units of time required by the algorithm in [Faleiro et al. PODC, 2012]
Byzantine Lattice Agreement in Asynchronous Systems
We study the Byzantine lattice agreement (BLA) problem in asynchronous distributed message passing systems. In the BLA problem, each process proposes a value from a join semi-lattice and needs to output a value also in the lattice such that all output values of correct processes lie on a chain despite the presence of Byzantine processes. We present an algorithm for this problem with round complexity of O(log f) which tolerates f < n/5 Byzantine failures in the asynchronous setting without digital signatures, where n is the number of processes. This is the first algorithm which has logarithmic round complexity for this problem in asynchronous setting. Before our work, Di Luna et al give an algorithm for this problem which takes O(f) rounds and tolerates f < n/3 Byzantine failures. We also show how this algorithm can be modified to work in the authenticated setting (i.e., with digital signatures) to tolerate f < n/3 Byzantine failures
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
A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice
Starting from a Cluster Variational Method, and inspired by the correctness
of the paramagnetic Ansatz (at high temperatures in general, and at any
temperature in the 2D Edwards-Anderson model) we propose a novel message
passing algorithm --- the Dual algorithm --- to estimate the marginal
probabilities of spin glasses on finite dimensional lattices. We show that in a
wide range of temperatures our algorithm compares very well with Monte Carlo
simulations, with the Double Loop algorithm and with exact calculation of the
ground state of 2D systems with bimodal and Gaussian interactions. Moreover it
is usually 100 times faster than other provably convergent methods, as the
Double Loop algorithm.Comment: 23 pages, 12 figures. v2: improved introductio
Linearizable Replicated State Machines With Lattice Agreement
This paper studies the lattice agreement problem in asynchronous systems and explores its application to building a linearizable replicated state machine (RSM). First, we propose an algorithm to solve the lattice agreement problem in O(log f) asynchronous rounds, where f is the number of crash failures that the system can tolerate. This is an exponential improvement over the previous best upper bound of O(f). Second, Faleiro et al have shown in [Faleiro et al. PODC, 2012] that combination of conflict-free data types and lattice agreement protocols can be applied to implement a linearizable RSM. They give a Paxos style lattice agreement protocol, which can be adapted to implement a linearizable RSM and guarantee that a command by a client can be learned in at most O(n) message delays, where n is the number of proposers. Later, Xiong et al in [Xiong et al. DISC, 2018] gave a lattice agreement protocol which improves the O(n) message delay guarantee to O(f). However, neither of the protocols is practical for building a linearizable RSM. Thus, in the second part of the paper, we first give an improved protocol based on the one proposed by Xiong et al. Then, we implement a simple linearizable RSM using our improved protocol and compare our implementation with an open source Java implementation of Paxos. Results show that better performance can be obtained by using lattice agreement based protocols to implement a linearizable RSM compared to traditional consensus based protocols
Characterizing and Improving Generalized Belief Propagation Algorithms on the 2D Edwards-Anderson Model
We study the performance of different message passing algorithms in the two
dimensional Edwards Anderson model. We show that the standard Belief
Propagation (BP) algorithm converges only at high temperature to a paramagnetic
solution. Then, we test a Generalized Belief Propagation (GBP) algorithm,
derived from a Cluster Variational Method (CVM) at the plaquette level. We
compare its performance with BP and with other algorithms derived under the
same approximation: Double Loop (DL) and a two-ways message passing algorithm
(HAK). The plaquette-CVM approximation improves BP in at least three ways: the
quality of the paramagnetic solution at high temperatures, a better estimate
(lower) for the critical temperature, and the fact that the GBP message passing
algorithm converges also to non paramagnetic solutions. The lack of convergence
of the standard GBP message passing algorithm at low temperatures seems to be
related to the implementation details and not to the appearance of long range
order. In fact, we prove that a gauge invariance of the constrained CVM free
energy can be exploited to derive a new message passing algorithm which
converges at even lower temperatures. In all its region of convergence this new
algorithm is faster than HAK and DL by some orders of magnitude.Comment: 19 pages, 13 figure
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