Summary: A non-topological proof for
the impossibility of k-set agreement
and Armando Casta~neda2
Department of Computer Science, Technion, Haifa 32000, Israel.
IRISA-INRIA, Campus de Beaulieu, 35042 Rennes Cedex, France.
Abstract. In the k-set agreement task each process proposes a value,
and it is required that each correct process has to decide a value which
was proposed and at most k distinct values must be decided. Using topo-
logical arguments it has been proved that k-set agreement is unsolvable
in the asynchronous wait-free read/write shared memory model, when
k < n, the number of processes.
This paper presents a simple, non-topological impossibility proof of k-set
agreement. The proof depends on two simple properties of the immediate
snapshot executions, a subset of all possible executions, and on the well
known graph theory result stating that every graph has an even number