Cartesian product

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cartesian product

[kär′tē·zhan ′präd·əkt]
(mathematics)
In reference to the product of P and Q, the set P × Q of all pairs (p,q), where p belongs to P and q belongs to Q.

Cartesian product

(mathematics)
(After Renee Descartes, French philosper and mathematician) The Cartesian product of two sets A and B is the set

A x B = a, b) | a in A, b in .

I.e. the product set contains all possible combinations of one element from each set. The idea can be extended to products of any number of sets.

If we consider the elements in sets A and B as points along perpendicular axes in a two-dimensional space then the elements of the product are the "Cartesian coordinates" of points in that space.

See also tuple.
References in periodicals archive ?
The measure of similarity corresponding to the Cartesian product
bar] of the Cartesian product USERS can be defined in accordance with theorem 2:
2) The number of tables in a query is determined per query, and if there are few tables available, the only way to get big results is through cartesian products.
In the figure this can be seen as the second join under the cartesian product is delegated to two separate nodes.
For instance, the children of the cartesian product are tagged as 1.
As observed in previous works, there is a trade-off between the communication and the efficiency of a parallel Join algorithm, as the whole Cartesian Product can be computed in one machine without any communication overhead.
The reason is that in [21] the proof for optimality is based on the assumption that the sub-part of the Cartesian Product that is executed by some machine is "rectangular" (i.
1) Computes a Cartesian Product of two tables AxB; (2) Restricts the resulting combinations only to those satisfying the function F,
For example, letting each process that computes a sub-part of the Cartesian Product, to select its data directly from the suitable database will result in a sequential bottleneck and will prevent us from getting the right execution times.
This is supported by the observation that during the experiments the Cartesian Product was completed long before the actual update to the database has completed.
TPC-H) as these do not include extensive Cartesian Product experiments.
Operating the sequential Cartesian Product algorithm obtains a minor speedup of 24.