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- W2963429582 abstract "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 {em 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. cite{attiya1995atomic} takes $log n$ synchronous rounds, and the algorithm by Mavronicolasa cite{mavronicolasabound} takes $min {O(h(L)), O(sqrt{f})}$ rounds. For asynchronous lattice agreement, we propose an algorithm which has time complexity of $2 cdot min {h(L), f + 1}$ 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 cite{faleiro2012generalized} 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 of Faleiro et al. cite{faleiro2012generalized}." @default.
- W2963429582 created "2019-07-30" @default.
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- W2963429582 date "2018-01-01" @default.
- W2963429582 modified "2023-09-30" @default.
- W2963429582 title "Lattice Agreement in Message Passing Systems." @default.
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