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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2018.41
URN: urn:nbn:de:0030-drops-98301
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9830/
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Zheng, Xiong ; Hu, Changyong ; Garg, Vijay K.

Lattice Agreement in Message Passing Systems

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LIPIcs-DISC-2018-41.pdf (0.5 MB)


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 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].

BibTeX - Entry

@InProceedings{zheng_et_al:LIPIcs:2018:9830,
  author =	{Xiong Zheng and Changyong Hu and Vijay K. Garg},
  title =	{{Lattice Agreement in Message Passing Systems}},
  booktitle =	{32nd International Symposium on Distributed Computing  (DISC 2018)},
  pages =	{41:1--41:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Ulrich Schmid and Josef Widder},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9830},
  URN =		{urn:nbn:de:0030-drops-98301},
  doi =		{10.4230/LIPIcs.DISC.2018.41},
  annote =	{Keywords: Lattice Agreement, Replicated State Machine, Consensus}
}

Keywords: Lattice Agreement, Replicated State Machine, Consensus
Seminar: 32nd International Symposium on Distributed Computing (DISC 2018)
Issue Date: 2018
Date of publication: 28.09.2018


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