Binary Search on a Tape

Given n records stored alphabetically on a tape, any comparison search procedure can be characterized by a binary tree. The complete binary tree (binary search) uses the minimum number of comparisons but not the minimum number of movements. The linear binary tree (sequential search) uses the minimum number of movements but not the minimum number of comparisons. A tape-optimal tree is a tree which minimizes the total cost of comparisons and movements. The tape-optimal tree is a “hybrid” of the linear tree and the complete binary tree, and is characterized for arbitrary n.