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Disk drives with movable two-headed arms are now commercially available. The two heads are separated by a fixed number of cylinders. A major problem for optimizing disk head movement, when answering database requests, is the specification of the optimum number of cylinders separating the two heads. An earlier analytical study assumed a FCFS model and concluded that the optimum separation distance should be equal to 0.44657 of the number of cylinders N of the disk. This paper considers that the SCAN scheduling policy is used in file access, and it applies combinatorial analysis to derive exact formulas for the expected head movement. Furthermore, it is proven that the optimum separation distance is N/2 -1 (TN/2 -11 and LN/2 -1 J) if N is even (odd). In addition, a comparison with a single-headed disk system operating under the same scheduling policy shows that if the two heads are optimally spaced, then the mean seek distance is less than one-half of the value obtained with one head. In fact that the SCAN policy is used for many database applications (for example, batching and secondary key retrieval) demonstrates the potential of two-headed disk systems for improving the performance of database systems.

Consider a file that resides in a linear storage device with one read head. Suppose that several queries on the file must be answered simultaneously with no prespecified order. To satisfy the ith query the head must be located at point I., of the file and traverse the file up to point R, without interruptions, where 1~ L, < R, 4 N denote positions in the file. We wish to find the execution order that minimizes the total time to service all queries. measured as the total distance traversed by the head. Although this is obviously a special type of traveling salesman problem. we show that the optimum sequence can be determined by a simple algorithm in G(n log n) time. The case in which the head may traverse a file in reverse is similarly solved.

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