The Communication Complexity of Atomic Commitment and of Gossiping

The problem of atomic commitment of a transaction in a distributed database is considered. This is a variant of the famous gossiping problem. Given a set of communication costs between pairs of participant sites, it is established that the necessary communication cost for any atomic commitment algorithm is twice the cost of a certain minimum spanning tree. This paper establishes the necessary communication time for any atomic commitment algorithm, given a set of communication delays between pairs of participant sites, and the time at which each participant completes its subtransaction. Then, it is determined that both lower bounds are also upper bounds in the following sense. There is an efficient (i.e., polynomial-time) algorithm that, in the absence of failures, has a minimum communication cost. There is another efficient algorithm that, in the absence of failures, has a minimum communication time. However, unless P = NP, there is no efficient algorithm which has a minimum communication complexity, name...