3,262 research outputs found
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
Distributed Computing in the Asynchronous LOCAL model
The LOCAL model is among the main models for studying locality in the
framework of distributed network computing. This model is however subject to
pertinent criticisms, including the facts that all nodes wake up
simultaneously, perform in lock steps, and are failure-free. We show that
relaxing these hypotheses to some extent does not hurt local computing. In
particular, we show that, for any construction task associated to a locally
checkable labeling (LCL), if is solvable in rounds in the LOCAL model,
then remains solvable in rounds in the asynchronous LOCAL model.
This improves the result by Casta\~neda et al. [SSS 2016], which was restricted
to 3-coloring the rings. More generally, the main contribution of this paper is
to show that, perhaps surprisingly, asynchrony and failures in the computations
do not restrict the power of the LOCAL model, as long as the communications
remain synchronous and failure-free
Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions
We consider the general problem of finding the minimum weight \bm-matching
on arbitrary graphs. We prove that, whenever the linear programming (LP)
relaxation of the problem has no fractional solutions, then the belief
propagation (BP) algorithm converges to the correct solution. We also show that
when the LP relaxation has a fractional solution then the BP algorithm can be
used to solve the LP relaxation. Our proof is based on the notion of graph
covers and extends the analysis of (Bayati-Shah-Sharma 2005 and Huang-Jebara
2007}.
These results are notable in the following regards: (1) It is one of a very
small number of proofs showing correctness of BP without any constraint on the
graph structure. (2) Variants of the proof work for both synchronous and
asynchronous BP; it is the first proof of convergence and correctness of an
asynchronous BP algorithm for a combinatorial optimization problem.Comment: 28 pages, 2 figures. Submitted to SIAM journal on Discrete
Mathematics on March 19, 2009; accepted for publication (in revised form)
August 30, 2010; published electronically July 1, 201
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