On the Space Complexity of Set Agreement

The k-set agreement problem is a generalization of the classical consensus problem in which processes are permitted to output up to k different input values. In a system of n processes, an m-obstruction-free solution to the problem requires termination only in executions where the number of processes taking steps is eventually bounded by m. This family of progress conditions generalizes wait-freedom (m = n) and obstruction-freedom (m = 1). In this paper, we prove upper and lower bounds on the number of registers required to solve m-obstruction-free k-set agreement, considering both one-shot and repeated formulations. In particular, we show that repeated k-set agreement can be solved using n + 2m - k registers and establish a nearly matching lower bound of n + m k.