You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
In multimedia, text or bioinformatics databases, applicat ions query sequences of n consecutive symbols called n-grams. Estimating the number of distinct n-grams is a view-size estimation problem. While view sizes can be estimated by sampling under statistical assumptions, we desire an unassuming algorithm with universally valid accuracy bounds. Most related work has focused on repeatedly hashing the data, which is prohibitive for large data sources. We prove that a one-pass one-hash algorithm is suffi cient for accurate estimates if the hashing is sufficiently independent. T o reduce costs further, we investigate recursive random hashing algorithms and show that they are sufficiently independent in practice. We compare our run ning times with exact counts using suffix arrays and show that, while we use ha rdly any storage, we are an order of magnitude faster. The approach further is extended to a one-pass one-hash computation of n-gram entropy and iceberg counts. The experiments use a large collection of English text from the Gutenberg Project as well as synthetic data.

Cited Abstract(s):
[1]: Accurately estimating the cardinality of aggregate views is crucial for logical and physical design of data warehouses. While the warehouse is under development and data are not available yet, the approaches based on accessing data cannot be adopted. This paper proposes an approach to estimate the cardinality of views based on a-priori information derived from the application domain. We face the problem by first computing satisfactory bounds for the cardinality, then by capitalizing on these bounds to determine a good probabilistic estimate for it. Bounds are determined by using, besides the functional dependencies expressed by the multidimensional scheme, additional domain-derived information in the form of cardinality constraints which may bound either the cardinality of a given view or the ratio between the cardinalities of two given views. In particular, we propose a bounding strategy which achieves an effective trade-off between the tightness of the bounds produced and the computational complexity.

[2]: 

[3]: On Line Analytical Processing (OLAP) aims at gaining useful information quickly from large amounts of data residing in a data warehouse. To improve the quickness of response to queries, pre-aggregation is a useful strategy. However, it is usually impossible to pre-aggregate along all combinations of the dimensions. The multi-dimensional aspects of the data lead to combinatorial explosion in the number and potential storage size of the aggregates. We must selectively pre-aggregate. Cost benefit analysis involves estimating the storage requirements of the aggregates in question. We present an original algorithm for estimating the number of rows in an aggregate based on the Pareto distribution model. We test the Pareto Model Algorithm empirically against three published algorithms, and conclude the Pareto Model Algorithm is consistently the best of these algorithms for estimating view size.

[4]: We provide several new sampling-based estimators of the number of distinct values of an attribute in a relation. We compare these new estimators to estimators from the database and statistical literature empirically, using a large number of attribute-value distributions drawn from a variety of real-world databases. This appears to be the first extensive comparison of distinct-value estimators in either the database or statistical literature, and is certainly the first to use highlyskewed data of the sort frequently encountered in database applications. Our experiments indicate that a new “hybrid” estimator yields the highest precision on average for a given sampling fraction. This estimator explicitly takes into account the degree of skew in the data and combines a new “smoothed jackknife” estimator with an estimator due to Shlosser. We investigate how the hybrid estimator behaves as we scale up the size of the database.

[5]: Accurately and efficiently estimating the number of distinct values for some attribute(s) or sets of attributes in a data set is of critical importance to many database operations, such as query optimization and approximation query answering. Previous work has focused on the estimation of the number of distinct values for a single attribute and most existing work adopts a data sampling approach. This paper addresses the equally important issue of estimating the number of distinct value combinations for multiple attributes which we call COLSCARD (for COLumn Set CARDinality). It also takes a different approach that uses existing statistical information (e.g., histograms) available on the individual attributes to assist estimation. We start with cases where exact frequency information on individual attributes is available, and present a pair of lower and upper bounds on COLSCARD that are consistent with the available information, as well as an estimator of COLSCARD based on probability. We then proceed to study the case where only partial information (in the form of histograms) is available on individual attributes, and show how the proposed estimator can be adapted to this case. We consider two types of widely used histograms and show how they can be constructed in order to obtain optimal approximation. An experimental evaluation of the proposed estimation method on synthetic as well as two real data sets is provided.

[6]: Accurately estimating the cardinality of aggregate views is crucial for logical and physical design of data warehouses. This paper proposes an approach based on cardinality constraints, derived a-priori from the application domain, which may bound either the cardinality of a view or the ratio between the cardinalities of two views. We face the problem by first computing satisfactory bounds for the cardinality, then by capitalizing on these bounds to determine a good probabilistic estimate for it. In particular, we propose a bounding strategy which achieves an effective trade-off between the tightness of the bounds produced and the computational complexity.
View-size estimation through sampling has been made adaptive by [4] : their strategy is to first attempt to determine whether the distribution is skewed and then use an appropriate statistical estimator. We can also count the marginal frequencies of each attribute value (or symbol in an @math -gram setting) and use them to give estimates as well as (exact) lower and upper bound on the view size [5] . Other researchers make particular assumptions on the distribution of relations [3] [1] [4]7 [2] .