Selection from read-only memory and sorting with optimum data movement

Abstract

The process of selecting an element of a given rank (for example, the median) from a given list is an important problem in computer science. Here, we consider the scenario when the given list resides in a read-only memory array and hence the elements cannot be moved within the array. We develop efficient deterministic and randomized algorithms for selection that use very little extra space (o(log n) number of extra storage cells). These algorithms complement the upper bounds for the time-space trade-offs obtained by Munro and Paterson[8] and Frederickson[3] who developed algorithms for selection in the same model when Ω((log n)²) extra storage cells are available. We apply our selection algorithms to obtain sorting algorithms that perform the optimum number of data movements on any given list, after deriving first this optimum bound for a given list. We also derive interesting upper bounds for time-space tradeoffs for sorting with optimum data movement.