cient Data Cubes for Dynamic

Data cubes provide aggregate information to support the analysis of the contents of data warehouses and databases. An important tool to analyze data in data cubes is the range query. For range queries that summarize large regions of massive data cubes, computing the query result on the y can result in non-interactive response times (e.g. in the order of minutes). To speed up range queries, values that summarize regions of the data cube are pre-computed and stored. This faster response time results in more expensive updates and/or space overhead. While the emphasis is typically on low query and update costs, growing data collections increase the demand for space-eecient approaches. In this paper two techniques are presented that have the same update and query costs as earlier approaches, without introducing any space overhead.