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Ordering Selection Operators Using the Minmax Regret Rule

Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance of their selectivities. The selectivities are modelled as intervals rather than exact values and we apply a concept from decision theory, the minimisation of the maximum regret, as a measure of optimality. We show that the associated decision problem is NP-hard, which renders a brute-force approach to solving it impractical. Nevertheless, by investigating properties of the problem and identifying special cases which can be solved in polynomial time, we gain insight that we use to develop a novel heuristic for solving the general problem. We also evaluate minmax regret query optimisation experimentally, showing that it outperforms a currently employed strategy of optimisers that uses mean values for uncertain parameters.