Reservoir sampling

Abstract: We introduce the problem of sampling from a moving window of recent items from a data stream and develop two algorithms for this problem. The first algorithm, "chain-sample", extends reservoir sampling to deal with the expiration of data elements from the sample. The expected memory usage of our algorithm is O(k) when maintaining a sample of size k over a window of the n most recent elements from the data stream, and with high probability the algorithm requires no more than O(k log n) memory.When the number of elements in the window is variable, as is the case when the size of the window is defined as a time duration rather than as a fixed number of data elements, the sampling problem becomes harder. Our second algorithm, "priority-sample", works even when the number of elements in the window can vary dynamically over time. With high probability, the "priority-sample" algorithm uses no more than O(k log n) memory.

Abstract: Computer clusters with the shared-nothing architecture are the major computing platforms for big data processing and analysis. In cluster computing, data partitioning and sampling are two fundamental strategies to speed up the computation of big data and increase scalability. In this paper, we present a comprehensive survey of the methods and techniques of data partitioning and sampling with respect to big data processing and analysis. We start with an overview of the mainstream big data frameworks on Hadoop clusters. The basic methods of data partitioning are then discussed including three classical horizontal partitioning schemes: range, hash, and random partitioning. Data partitioning on Hadoop clusters is also discussed with a summary of new strategies for big data partitioning, including the new Random Sample Partition (RSP) distributed model. The classical methods of data sampling are then investigated, including simple random sampling, stratified sampling, and reservoir sampling. Two common methods of big data sampling on computing clusters are also discussed: record-level sampling and block-level sampling. Record-level sampling is not as efficient as block-level sampling on big distributed data. On the other hand, block-level sampling on data blocks generated with the classical data partitioning methods does not necessarily produce good representative samples for approximate computing of big data. In this survey, we also summarize the prevailing strategies and related work on sampling-based approximation on Hadoop clusters. We believe that data partitioning and sampling should be considered together to build approximate cluster computing frameworks that are reliable in both the computational and statistical respects.

Abstract: This paper reviews recent literature on techniques for obtaining random samples from databases. We begin with a discussion of why one would want to include sampling facilities in database management systems. We then review basic sampling techniques used in constructing DBMS sampling algorithms, e.g. acceptance/rejection and reservoir sampling. A discussion of sampling from various data structures follows: B + trees, hash files, spatial data structures (including R-trees and quadtrees). Algorithms for sampling from simple relational queries, e.g. single relational operators such as selection, intersection, union, set difference, projection, and join are then described. We then describe sampling for estimation of aggregates (e.g. the size of query results). Here we discuss both clustered sampling, and sequential sampling approaches. Decision-theoretic approaches to sampling for query optimization are reviewed.