Synchronous Set Agreement: a Concise Guided Tour (with open problems)

The $k$-set agreement problem is a paradigm of coordination problems encountered in distributed computing. The parameter $k$ defines the coordination degree we are interested in. The case $k=1$ corresponds to the well-known uniform consensus problem. More precisely, the $k$-set agreement problem considers a system made up of $n$ processes where each process proposes a value. It requires that each non-faulty process decides a value such that a decided value is a proposed value, and no more than $k$ different values are decided. This paper visits the $k$-set agreement problem in synchronous systems where up to $t$ processes can experience failures. Three failure models are explored: the crash failure model, the send omission failure model, and the general omission failure model. Lower bounds and protocols are presented for each model. Open problems for the general omission failure model are stated. This paper can be seen as a short tutorial whose aim is to make the reader familiar with the $k$-set agreement problem in synchrony models with increasing fault severity. An important concern of the paper is simplicity. In addition to its survey flavor, several results and protocols that are presented are new. \\ Ce rapport constitue une visite guide de l'accord ensembliste synchrone en presence de crashs, de fautes d'omission en emission, et de fautes d'omission en emission et reception.