Finding modes with equality comparisons

We give three algorithms for finding mode, including one that is a generalization of a classical majority finding algorithm due to Fischer and Salzberg (1982) [9]. We also discuss upper and lower bounds for sorting (i.e., finding the frequency of every element) and for finding the least frequent element. Sorting problem (under the equality comparisons) also known as equivalence class sorting, has applications in several scenarios where the total order of elements is either not possible or can not be revealed for security reasons.