Lattice Agreement in Message Passing Systems
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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 f and {O(^2 h(L)), O(^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. attiya1995atomic takes n synchronous rounds, and the algorithm by Mavronicolasa mavronicolasabound takes {O(h(L)), O(√(f))} rounds. For asynchronous lattice agreement, we propose an algorithm which has time complexity of 2 ·{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 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 {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. faleiro2012generalized.
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