On the Worst Case Data Sets for Order Statistics

In this work, we consider the selection algorithms for the order statistics problems. A general partition based selection algorithm can be made to go quadratic by constructing input on the fly in response to the sequence of items compared. We develop an extremely simple class for constructing the worst case data set for the partition based selection algorithm. The general method works against any implementation of partition based selection algorithm that satisfies certain very mild and realistic assumptions. Computational results ascertain that the techniques developed are not only of theoretical interest, but also may actually lead to the worst case data sets for general partition based selection algorithms