Recent data stream systems such as TelegraphCQ have employed the well-known property of duality between data and queries. In these systems, query processing methods are classified into two dual categories ? data-initiative and query-initiative ? depending on whether query processing is initiated by selecting a data element or a query. Although the duality property has been widely recognized, previous data stream systems do not fully take advantages of this property since they use the two dual methods independently: data-initiative methods only for continuous queries and query-initiative methods only for ad-hoc queries. We contend that continuous query processing can be better optimized by adopting an approach that integrates the two dual methods. Our primary contribution is based on the observation that spatial join is a powerful tool for achieving this objective. In this paper, we first present a new viewpoint of transforming the continuous query processing problem to a multi-dimensi...