Abstract

This paper is about the hardness of Leader Election problem in asynchronous distributed systems in which processes can crash but links are reliable. Recently, the hardness of a problem encountered in the systems is defined with respect to the difficulty to solve it despite failures: a problem is easy if it can be solved in presence of failures, otherwise it is hard [9]. It is shown in [9] that problems are classified as three classes: F (fault-tolerant), NF (Not fault-tolerant) and NFC (NF-completeness). Among those, the class NFC is the hardest problem to solve. It is also shown in [9] that the construction of Perfect Failure Detector (problem P) belongs to NFC. In this paper, we show that Leader Election is also one of NFC problems by using a general reduction protocol that reduces the Leader Election Problem to P. We use a formulation of the Leader Election problem as a prototype to show that it belongs to NFC.