Heaps and heapsort on secondary storage

Abstract

A heap structure designed for secondary storage is suggested that tries to make the best use of the available buffer space in primary memory. The heap is a complete multi-way tree, with multi-page blocks of records as nodes, satisfying a generalized heap property. A special feature of the tree is that the nodes may be partially filled, as in B-trees. The structure is complemented with priority-queue operations insert and delete-max. When handling a sequence of S operations, the number of page transfers performed is shown to be O(∑ i = 1 S( 1 P ) log ( M P ) ( N i P )) , where P denotes the number of records fitting into a page, M the capacity of the buffer space in records, and N i , the number of records in the heap prior to the ith operation (assuming P ⩾ 1 and S > M ⩾ c · P, where c is a small positive constant). The number of comparisons required when handling the sequence is O(∑ i = 1 S log 2 N i ). Using the suggested data structure we obtain an optimal external heapsort that performs O(( N P ) log ( M P ) ( N P )) page transfers and O( N log 2 N) comparisons in the worst case when sorting N records.