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In the fields of databases and transaction processing (transaction management), a schedule (or history) of a system is an abstract model to describe the order of executions in a set of transactions running in the system. Often it is a list of operations (actions) ordered by time, performed by a set of transactions that are executed together in ...
Given a set and a partial order relation, typically the non-strict partial order , we may uniquely extend our notation to define four partial order relations , <,, and >, where is a non-strict partial order relation on , < is the associated strict partial order relation on (the irreflexive kernel of ), is the dual of , and > is the dual of <.
Join and meet are dual to one another with respect to order inversion. A partially ordered set in which all pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice.
However, since database systems schedule their transactions independently, it is possible that the transactions' precedence orders in two databases or more are not compatible (no global partial order exists that can embed the respective local partial orders together). With CO, precedence orders are also the commitment orders.
The identity relation = on any set is also a partial order in which every two distinct elements are incomparable. It is also the only relation that is both a partial order and an equivalence relation because it satisfies both the antisymmetry property of partial orders and the symmetry property of equivalence relations. Many advanced properties ...
A strict order on a set is a homogeneous relation arising in order theory. In 1951 Jacques Riguet adopted the ordering of an integer partition, called a Ferrers diagram, to extend ordering to binary relations in general. [47] The corresponding logical matrix of a general binary relation has rows which finish with a sequence of ones.
Let and be relations where | | < | |. fits in pages memory and fits in pages memory. In the worst case, a sort-merge join will run in (+) I/O operations. In the case that and are not ordered the worst case time cost will contain additional terms of sorting time: (+ + + ()), which equals ( + ()) (as linearithmic terms outweigh the linear terms, see Big O notation – Orders of ...
In database theory, a relation, as originally defined by E. F. Codd, [1] is a set of tuples (d 1,d 2,...,d n), where each element d j is a member of D j, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation.