Annotations in Data Streams

The central goal of data stream algorithms is to process massive streams of data using sublinear storage space. Motivated by work in the database community on outsourcing database and data stream processing, we ask whether the space usage of such algorithms be further reduced by enlisting a more powerful "helper" who can annotate the stream as it is read. We do not wish to blindly trust the helper, so we require that the algorithm be convinced of having computed a correct answer. We show upper bounds that achieve a non-trivial tradeoff between the amount of annotation used and the space required to verify it. We also prove lower bounds on such tradeoffs, often nearly matching the upper bounds, via notions related to Merlin-Arthur communication complexity. Our results cover the classic data stream problems of selection, frequency moments, and fundamental graph problems such as triangle-freeness and connectivity. Our work is also part of a growing trend -- including recent stu...

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Amit Chakrabarti, Graham Cormode, Andrew McGregor
• Keywords: Data Stream Algorithms, Data Stream Problems, Data Stream Processing, ICALP 2009, Theoretical Computer Science