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We introduce a stronger validity property for the byzantine agreement problem with orderable initial values: The median validity property. In particular, the decision value is required to be close to the median of the initial values of the non-byzantine nodes. The proximity to the median scales with the desired level of fault-tolerance: If no fault-tolerance is required, algorithms have to decide for the true median. If the number of failures is maximal, algorithms must still decide on a value within the range of the input values of the non-byzantine nodes. We present a deterministic algorithm satisfying this property for n >= 3t+1 within t+1 phases, where t is the maximum number of byzantine nodes and n is the total number of nodes.
@InProceedings{stolz_et_al:LIPIcs.OPODIS.2015.22,
author = {Stolz, David and Wattenhofer, Roger},
title = {{Byzantine Agreement with Median Validity}},
booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
pages = {22:1--22:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-98-9},
ISSN = {1868-8969},
year = {2016},
volume = {46},
editor = {Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.22},
URN = {urn:nbn:de:0030-drops-65911},
doi = {10.4230/LIPIcs.OPODIS.2015.22},
annote = {Keywords: Reliability, fault-tolerance, median, consensus}
}