Approximate Counts and Quantiles over Sliding Windows

We consider the problem of maintaining approximate counts and quantiles over fixed- and variablesize sliding windows in limited space. For quantiles, we present deterministic algorithms whose space requirements are O(1 log 1 log N) and O(1 log 1 log N log N) in the worst-case for fixed- and variablesize windows, respectively, where N denotes the current number of elements in the window. Our space bounds improve upon the previous best bounds of O( 1 2 polylog(1 , N)). For counts, we present both deterministic and randomized algorithms. The deterministic algorithms require O(1 log2 1 ) and O(1 log2 1 log N) worst-case space for fixed- and variable-size windows, respectively, while the randomized ones require O(1 log 1 ) and O(1 log 1 log N) worst-case space. We believe no previous work on space-efficient approximate counts for sliding windows exists.

• Type: Conference
• Year: 2004
• Where: PODS
• Authors: Arvind Arasu, Gurmeet Singh Manku
• Keywords: Database, Deterministic Algorithms, PODS 2004, Space-efficient Approximate Counts, Worst-case Space