Perhaps the most flexible synopsis of a database is a uniform random sample of the data; such samples are widely used to speed up processing of analytic queries and data-mining tasks, enhance query optimization, and facilitate information integration. The ability to bound the maximum size of a sample can be very convenient from a system-design point of view, because the task of memory management is simplified, especially when many samples are maintained simultaneously. In this paper, we study methods for incrementally maintaining a bounded-size uniform random sample of the items in a dataset in the presence of an arbitrary sequence of insertions and deletions. For “stable” datasets whose size remains roughly constant over time, we provide a novel sampling scheme, called “random pairing” (RP), that maintains a bounded-size uniform sample by using newly inserted data items to compensate for previous deletions. The RP algorithm is the first extension of the 45-year-old reservoir sampling algorithm to handle deletions; RP reduces to the “passive” algorithm of Babcock et al. when the insertions and deletions correspond to a moving window over a data stream. Experiments show that, when dataset-size fluctuations over time are not too extreme, RP is the algorithm of choice with respect to speed and sample-size stability. For “growing” datasets, we consider algorithms for periodically resizing a bounded-size random sample upwards. We prove that any such algorithm cannot avoid accessing the base data, and provide a novel resizing algorithm that minimizes the time needed to increase the sample size. We also show how to merge uniform samples from disjoint datasets to obtain a uniform sample of the union of the datasets; the merged sample can be incrementally maintained. Our new RPMerge algorithm extends the HRMerge algorithm of Brown and Haas to effectively deal with deletions, thereby facilitating efficient parallel sampling.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:82220 |
| Date | 12 January 2023 |
| Creators | Gemulla, Rainer, Lehner, Wolfgang, Haas, Peter J. |
| Publisher | Springer |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/acceptedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 0949-877X, 10.1007/s00778-007-0065-y |
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