An Information-Theoretic Study on Aggregate Responses

An enumeration of individual objects is not always the best means of infonnation exchange. This papiz concerns the problem of providing aggregate responses to database queries. An aggregate response is an expression whose terms an3 quantified concepts. The tradeoff between the conciseness and preciseness of an aggregate response is studied. Conciseness is measured by the length (the number of terms) of an expression, and preciseness is measured by the entropy or the amount of uncertainty associated with the expression. For a given length, an expression with the minimum amount of entropy is called optimal. Under a one-level taxonomy with the same cardinaliries for all leaf concepts, the problem of tinding an op timal expression can be solved inexpensively. An efficient heuristic is also proposed for the general one-level taxonomy. For a taxonomy of more than one level, an efficient heuristic is suggested which experiments indicate yields good solutions.