A database allows its users to reduce uncertainty about the world. However, not all properties of all objects can always be stored in a database. As a result, the user may have to use probabilistic inference rules to estimate the data required for his decisions. A decision based on such estimated data may not be perfect. The authors call the costs associated with such suboptimal decisions the cost of incomplete information. This cost can be reduced by expanding the database to contain more information; such expansion will increase the data-related costs because of more data collection, manipulation, storage, and retrieval. A database designer must then consider the trade-off between the cost of incomplete information and the data-related costs, and choose a design that minimizes the overall cost to the organization. In temporal databases, the sheer volume of the data involved makes such a trade-off at design time all the more important. They develop probabilistic inference rules that allow one to infer missing values in spatial, as well as temporal, dimension. They then use the framework for developing guidelines for designing and reorganizing temporal databases, which explicitly includes a trade-off between the incomplete information and the data-related costs.

The exact expression for the expected number of disk accesses required to retrieve a given number of records, called the Yao function, requires iterative computations. Several authors have developed approximations to the Yao function, all of which have substantial errors in some situations. We derive and evaluate simple upper and lower bounds that never differ by more than a small fraction of a disk access.>

This paper presents a methodology for trading-off the cost of incomplete information against the data-related costs in the design of database systems. It investigates how the usage patterns of the database, defined by the characteristics of information requests presented to it, affect its conceptual design. The construction of minimum-cost answers to information requests for a variety of query types and cost structures is also studied. The resulting costs of incomplete database information are balanced against the data-related costs in the derivation of the optimal design.