Abstract
The problem of statistics and aggregate maintenance over data streams has gained popularity in recent years especially in telecommunications network monitoring, trend-related analysis, web-click streams, stock tickers, and other time-variant data. The amount of data generated in such applications can become too large to store, or if stored too large to scan multiple times. We consider queries over data streams that are biased towards the more recent values. We develop a technique that summarizes a dynamic stream incrementally at multiple resolutions. This approximation can be used to answer point queries, range queries, and inner product queries. Moreover, the precision of answers can be changed adaptively by a client. Later, we extend the above technique to work in a distributed setting, specifically in a large network where a central site summarizes the stream and clients ask queries. We minimize the message overhead by deciding what and where to replicate by using an adaptive replication scheme. We maintain a hierarchy of approximations that change adaptively based on the query and update rates. We show experimentally that our technique performs better than existing techniques: up to 50 times better in terms of approximation quality, up to four orders of magnitude times better in response time, and up to five times better in terms of message complexity.