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We consider a problem of finding optimized transitive association rules. A transitive association rule is a transitive sequence of different events. Each of two consecutive events in a transitive association rule is a conventional association rule. Transitive confidence is the product of confidence values of all the association rules in the event sequence. The optimized transitive association rule from a cause event to an effect event is the optimal sequence of events whose transitive confidence is maximum among all possible sequences from the cause to the effect. In this paper, we present space efficient algorithms for computing all of the optimized transitive association rules between events, whose transitive confidence is not less than a user specified minimum confidence value.