Date: 26 May 2005

Heapsort—Adapted for presorted files

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We provide a new sorting algorithm which is optimal with respect to several known, and new, measures of presortedness. A new such measure, called Osc(X), measures the oscillation within the input data. The measure has an interesting application in the sweep-line technique in computational geometry. Our algorithm is based on a new approach which yields space efficiency and it uses simple data structures. For example, after a linear time preprocessing step, the only data structures used are a static tree and a heap.