 
Summary: WaitFree nset Consensus when Inputs are
Restricted
Hagit Attiya and Zvi Avidor
Department of Computer Science
The Technion, Haifa 32000, Israel
fhagit,azvig@technion.ac.il
Abstract. The kset consensus problem requires processes to decide on
at most k of their input values. The problem can be solved using only
read / write operations in the presence of f crash failures if and only if
f ! k. One way to subvert this impossibility result is to restrict the set
of possible assignments of input values to processes. This paper presents
a characterization of the input restrictions that allow a waitfree solution
of nset consensus in a system with n + 1 processes, using only read and
write operations.
1 Introduction
The kset consensus problem [1] requires nonfaulty processes to decide on at
most k different values, so that every decision value is some process's input.
The kset consensus problem is solvable in an asynchronous system subject to f
crash failures using read/write operations if and only if f ! k. An algorithm 1 was
presented in [1] while the lower bound was proved in three independent papers [2
