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An effective method for determining consensus in large collectives

Nowadays, using the consensus of collectives for solving problems plays an
 essential role in our lives. The rapid development of information technology
 has facilitated the collection of distributed knowledge from autonomous
 sources to find solutions to problems. Consequently, the size of collectives
 has increased rapidly. Determining consensus for a large collective is very
 time-consuming and expensive. Thus, this study proposes a vertical partition
 method (VPM) to find consensus in large collectives. In the VPM, the primary
 collective is first vertically partitioned into small parts. Then, a
 consensus-based algorithm is used to determine the consensus for each smaller
 part. Finally, the consensus of the collective is determined based on the
 consensuses of the smaller parts. The study demonstrates, both theoretically
 and experimentally, that the computational complexity of the VPM is lower
 than 57.1% that of the basic consensus method. This ratio reduces quickly if
 the number of smaller parts reduces.