Lower bounds for synchronous networks and the advantage of local information
For a natural, fairly general class of algorithms that solve a global problem like election in n-node m-link synchronous networks with local information we rigorously prove a lower bound Ω(m) for the number of messages that have to be exchanged among the processors. Without local information the lower bound becomes exactly m. This result matches (up to constant factors) the known upper bounds that hold even for asynchronous networks without local information. Further it is shown that relaxing any condition imposed on the algorithms one can design artificial protocols with message complexity O(n log n).
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