Association rule mining is an indispensable tool for discovering insights from large databases and data warehouses. The data in a warehouse being multi-dimensional, it is often useful to mine rules over subsets of data defined by selections over the dimensions. Such interactive rule mining over multi-dimensional query windows is difficult since rule mining is computationally expensive. Current methods using pre-computation of frequent itemsets require counting of some itemsets by revisiting the transaction database at query time, which is very expensive. We develop a method (RMW) that identifies the minimal set of itemsets to compute and store for each cell, so that rule mining over any query window may be performed without going back to the transaction database. We give formal proofs that the set of itemsets chosen by RMW is sufficient to answer any query and also prove that it is the optimal set to be computed for 1 dimensional queries. We demonstrate through an extensive empirical evaluation that RMW achieves extremely fast query response time compared to existing methods, with only moderate overhead in pre-computation and storage. Copyright © SIAM.