 
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
