Optimal Elections in Faulty Loop Networks and Applications

Loop networks (or Hamiltonian circulant graphs) are a popular class of faulttolerant 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 has 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 non-faulty networks with sense of direction. keywords Loop Networks, Leader Election, Fault-Tolerance, Interconnection Networks, Distributed Algorithms, Sense of Direction. This research supported in part by N.S.E.R.C, grant#A2415, and by Macquarie Research Grant “Structural Information in Networks”. Some of the results of this work have been presented at the 24th IEEE Annual International Symposium on Fault-Tolerant Computing (FTCS’94), and at the 14th IEEE International Conference on Distributed Computing Systems (ICDCS’94). Dept. of Computing, School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, NSW 2109, Australia. Fax: 61-2-9850 9574. Email: [email protected] School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6 Canada. Email: [email protected]