Summary: A Direct Lower Bound for k­Set Consensus
Hagit Attiya
Department of Computer Science, The Technion
The k­set consensus problem [4] requires that all
nonfaulty processors decide on a small set of differ­
ent values (of size k), and that every decision value be
some processor's original input. This problem is solv­
able in an asynchronous system subject to crash fail­
ures using only read and write operations, if and only
if f ! k, where f is the number of faults to be toler­
ated. An algorithm was presented by Chaudhuri [4].
while the lower bound was proved (independently) in
three papers [3, 5, 6].
Both Borowsky and Gafni [3] and Saks and Za­
haroglou [6] restrict attention to executions in which
processors take steps in blocks. In [3], there is a
graph representation in which each node corresponds
to the view of a single processor in a specific block
execution, and there are edges between views that
appear in the same execution; then, this graph is

Source: Attiya, Hagit - Department of Computer Science, Technion, Israel Institute of Technology

Collections: Computer Technologies and Information Sciences