COPING WITH ERRONEOUS INFORMATION WHILE SORTING

In this correspondence, we study the problem of sorting n distinct elements in ascending sequence according to a total order, using comparison queries which receive "yes" or "no" answers, but as many as e of which may be erroneous. In a half-lie version, all "yes" answers are guaranteed to be correct and the errors are confined to "no" answers. We show that the comparison query complexity of the sorting problem for this case is OMEGA (n log n + e) and then demonstrate an asymptotically optimal algorithm. In a full-lie version, however, both "yes" and "no" answers can be false. We show that the comparison query complexity of the sorting problem for this case is OMEGA(n log n + en) and then demonstrate an algorithm which generalizes the familiar binary insertion sort technique. This algorithm is asymptotically optimal if e = O(n).