Complexity Of The 3ROM Algorithm Sample Clauses

Complexity Of The 3ROM Algorithm. In 3ROM algorithm, since a node does not send a message to itself, the number of transmitted messages per node and for each round is (K-1). For the worst case analysis, all nodes participate in Rounds 2 and 3. Thus, the total number of messages transmitted per round is (K-1), K(K-1), and K2(K-1), for Rounds 1, 2 and 3, respectively. Although in Round 3 a node broadcasts a vector of messages, for complexity analysis purposes, we count each individual message separately. Therefore, the total number of exchanged messages is (K-1)+K(K-1)+K2(K-1) and the message complexity for the 3ROM algorithm is O(K3). However, if a message is indeed physically broadcast to all, e.g., when the communication means is wireless, then the number of broadcast messages per node for each round is 1. Thus, the total number of messages broadcast per round is 1, (K-1), and K(K-1), for Rounds 1, 2 and 3, respectively, the total number of exchanged messages is 1+(K-1)+K(K-1), and the message complexity for the 3ROM algorithm is O(K2). However, the message complexity for the OM algorithm for the above two scenarios is O(KF) and O(KF-1), respectively. We would like to emphasize that the number of rounds of exchanged messages for the 3ROM algorithm is independent of F.
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