On the Hardness of Leader Election in Asynchronous Distributed Systems with Crash Failures

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.