Heaps and Heapsort on Secondary Storage

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 ( ∑S i=1 (1/P ) log(M/P ) (Ni/P ) ) , where P denotes the number of records fitting into a page, M the capacity of the buffer space in records, and Ni 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 (