Optimal tradeoffs between time and bit complexity in distributed synchronous rings

Abstract

We consider the problem of leader election in ring of n processors with both known and unknown ring size and related problems. Most algorithms transmit processor-ids and therefore their bit complexity incresases logarithmically in these numbers. For synchronous rings algorithms have been found that use a kind of waiting technique which makes the bit complexity independent of the processor-ids. For those algorithms, however, the run time depends on the processor-ids. This paper proves that this must be the case establishing a tradeoff between the two complexity measures. We show lower bounds and describe a class of algorithms that almost meet the lower bounds. Moreover, for bounded size messages our algorithm is faster than any known one.

Research supported by DFG grant RE 672 / 1–2