Brief Announcement: Partition Approach to Failure Detectors for k-Set Agreement

There have been several studies on failure detectors for solving k-set agreement, a problem that requires n processes to decide on at most k (k < n) values proposed by the n processes in systems where processes may fail by crashing. In particular, Mostefaoui et.al. study the relationship among these failure detector classes and show that class Ωk is the weakest among them to solve k-set agreement [5]. Ωk was further conjectured in [6] to be the weakest failure detector for k-set agreement in the shared-memory model for all k > 1. In the message-passing model, It is shown in [5] that a majority of correct processes is necessary to solve kset agreement with Ωk. The majority requirement can be translated to the requirement of quorum failure detectors Σ [3]. Therefore, one may ask whether Ωk×Σ is the weakest failure detector for k-set agreement in the message-passing model, or whether Ωk is the weakest failure detector for k-set agreement in the message-passing model augmented with Σ, when k > 1. In this announcement, we report our study in [2], in which we introduce the partition approach to define weaker failure detectors for k-set agreement in the message-passing model. We apply the partition approach and propose two partitioned failure detectors Πk and Π S k , and show that they are strong enough to solve k-set agreement but are strictly