Optimal fault-tolerant leader election in chordal rings

Chordal rings (or circulant graphs) are a popular class of fault-tolerant network topologies which include rings and complete graphs. For this class, the fundamental problem of leader election has been extensively studied assuming either a fault-free system or an upper-bound on the number of link failures. We consider chordal rings where an arbitrary number of lines has failed and a processor can only detect the status of its incident links. We shows that a leader election protocol in a faulty chordal ring requires only O(n log n) messages in the worst-case, where n is the number of processors. Moreover, we show that this is optimal. If the network is not partitioned, the algorithm will detect it and will elect a leader. In case the failures have partitioned the network a distinctive element will be determined in each active component and will detect that a partition has occurred; depending on the application, these distinctive elements can thus take the appropriate actions.<>