Optimal elections in faulty loop networks and applications

Loop networks (or Hamiltonian 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 loop networks where an arbitrary number of links have failed and a processor can only detect the status of its incident links. We show that a leader election protocol In a faulty loop network 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. The proposed algorithm also detects network partitions. We also show that it provides an optimal solution for arbitrary nonfaulty networks with sense of direction.