Invited Paper: On the Cost-Optimal Parallel Solution of the Majority Problem

The majority problem can be stated as follows: there is a collection of n bank cards that belong to different bank accounts. The only way to “read” these cards is through one or more two-input “equivalence testers”. Each tester accepts two cards and outputs “yes” if two input cards correspond to the same bank account or “no” if they do not. The objective of the majority problem is to design a solution that uses the minimum number of tests to determine if more than $n/2$ cards belong to the same bank account and then find these cards. We first review two sequential solutions, including the Boyer-Moore optimal linear solution (i.e., with a time complexity of $O(n))$. Then, we introduce an optimal elimination solution together with a special structure to support a cost-optimal parallel solution that solves the problem in $O(\log n)$ using $O(n/ \log n)$ processors (i.e., testers). That is, this solution matches the optimal sequential solution with $O(n)$ operations.