Data Streams with Bounded Deletions
Rajesh Jayaram, David P. Woodruff

TL;DR
This paper introduces an intermediate data stream model characterized by a parameter alpha, bridging insertion-only and turnstile models, enabling more space-efficient algorithms for fundamental streaming problems when streams have bounded deletions.
Contribution
The authors propose the alpha-property model, providing a unified framework that reduces space complexity from logarithmic in n to logarithmic in alpha for key streaming tasks.
Findings
Space complexity reduced to O(log(alpha)) for many problems
Matching or nearly matching lower bounds established for alpha-property streams
Many real-world turnstile streams are alpha-property, making results practically significant
Abstract
Two prevalent models in the data stream literature are the insertion-only and turnstile models. Unfortunately, many important streaming problems require a multiplicative factor more space for turnstile streams than for insertion-only streams. This complexity gap often arises because the underlying frequency vector is very close to , after accounting for all insertions and deletions to items. Signal detection in such streams is difficult, given the large number of deletions. In this work, we propose an intermediate model which, given a parameter , lower bounds the norm by a -fraction of the mass of the stream had all updates been positive. Here, for a vector , , and the value of we choose depends on the application. This gives a fluid medium between insertion…
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