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The cardinality or "size" of a multiset is the sum of the multiplicities of all its elements. For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6.
The HyperLogLog has three main operations: add to add a new element to the set, count to obtain the cardinality of the set and merge to obtain the union of two sets. Some derived operations can be computed using the inclusion–exclusion principle like the cardinality of the intersection or the cardinality of the difference between two HyperLogLogs combining the merge and count operations.
Within data modelling, cardinality is the numerical relationship between rows of one table and rows in another. Common cardinalities include one-to-one , one-to-many , and many-to-many . Cardinality can be used to define data models as well as analyze entities within datasets.
An example of a data table column with high-cardinality would be a USERS table with a column named USER_ID. This column would contain unique values of 1- n . Each time a new user is created in the USERS table, a new number would be created in the USER_ID column to identify them uniquely.
For example, think of A as Authors, and B as Books. An Author can write several Books, and a Book can be written by several Authors. In a relational database management system, such relationships are usually implemented by means of an associative table (also known as join table, junction table or cross-reference table), say, AB with two one-to-many relationships A → AB and B → AB.
The algorithm was introduced by Philippe Flajolet and G. Nigel Martin in their 1984 article "Probabilistic Counting Algorithms for Data Base Applications". [1] Later it has been refined in "LogLog counting of large cardinalities" by Marianne Durand and Philippe Flajolet , [ 2 ] and " HyperLogLog : The analysis of a near-optimal cardinality ...
Barker's notation refers to the ERD notation developed by Richard Barker, Ian Palmer, Harry Ellis et al. whilst working at the British consulting firm CACI around 1981. The notation was adopted by Barker when he joined Oracle and is effectively defined in his book Entity Relationship Modelling as part of the CASE Method series of books.
In some cases a multiset in this counting sense may be generalized to allow negative values, as in Python. C++'s Standard Template Library implements both sorted and unsorted multisets. It provides the multiset class for the sorted multiset, as a kind of associative container, which implements this multiset using a self-balancing binary search ...