The Optimum Execution Order of Queries in Linear Storage

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.