Robert M. Losee,
Upper Bounds for Retrieval Performance and Their Use Measuring Performance and Generating Optimal Boolean Queries: Can it Get Any Better Than This?
Information Processing & Management, 30(2), p. 193-204, 1994.

Abstract:

The best-case, worst-case, and random document rankings and retrieval performance may be determined given a method discussed here. A method for deriving the optimal Boolean query for a given level of recall is suggested, as is a method for determining the quality of a Boolean query. Measures are proposed that modify conventional text retrieval or search engine measures such as precision, E, and average search length so that the values for these measures are $1$ when retrieval is optimal, $0$ when retrieval is random, and $-1$ when worst-case. Tests using one of these measures show that many retrievals are optimal. Consequences for retrieval research are examined.

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