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Discovery of association rules has been found useful in many applications. In previous work, all items in a basket database are treated uniformly. We generalize this to the case where items are given weights to reflect their importance to the user. The weights may correspond to special promotions on some products, or the profitability of different items. We can mine the weighted association rules with weights. The downward closure property of the support measure in the unweighted case no longer exists and previous algorithms cannot be applied. In this paper, two new algorithms are introduced to handle this problem. In these algorithms we make use of a metric called the k-support bound in the mining process. Experimental results show the efficiency of the algorithms for large databases.