Efficient elections in chordal ring networks

We study the message complexity of the problem of distributively electing a leader in chordal rings. Such networks consist of a basic ring with additional links, the extreme cases being the oriented ring and the complete graph with a full sense of direction. We present a general election algorithm for these networks, and prove its optimality. As a corollary, we show thatO(logn) chords at each processor suffice to obtain an algorithm that uses at mostO(n) messages; this improves and extends a previous work, where an algorithm, also usingO(n) messages, was suggested for the case where alln-1 chords exist (the oriented complete network).