A brief note on minimax optimal trees

Abstract

The paper addresses the problem of finding doubly-chained tree structures for data storage which are best in the sense of minimizing maximum search time as opposed to the usual objective of minimizing average search time.

The feasibility of pursuing the latter invariably rests upon assuming a uniform distribution of inquiries, which is often not a valid assumption. As a result, some situations might be treated more appropriately by seeking solutions that minimize maximum search times. It is shown that for the case of equally costly horizontal and vertical search steps, the solution found for minimizing the average is at the same time a minimax solution. In the more general case, that is not necessarily so, but a minimax solution is easily found.