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The data sets contain the same number of records. The corresponding records and keys are identical. For partitioned data sets, IEBCOMPR considers the data sets equal if the following conditions are met: The directory entries for the two partitioned data sets match - that is, the names are the same, and the number of entries are equal.
There is an edge between a set and an element, iff the set contains the element. This graph has the following properties: If two sets intersect, the distance between them is 2 (from one set, to an element in the intersection, to the other set). If two sets do not intersect, the distance between them is at least 4.
Some definitions eschew the separate oracle tape. When the oracle state is entered, a tape symbol is specified. The oracle is queried with the number of times that this tape symbol appears on the work tape. If that number is in the oracle set, the next state is the YES state; if it is not, the next state is the NO state. [2]
Vertical partitioning involves creating tables with fewer columns and using additional tables to store the remaining columns. [2] Generally, this practice is known as normalization . However, vertical partitioning extends further, and partitions columns even when already normalized.
Partitions of a 4-element set ordered by refinement. A partition α of a set X is a refinement of a partition ρ of X—and we say that α is finer than ρ and that ρ is coarser than α—if every element of α is a subset of some element of ρ. Informally, this means that α is a further fragmentation of ρ. In that case, it is written that ...
The partition problem - a special case of multiway number partitioning in which the number of subsets is 2. The 3-partition problem - a different and harder problem, in which the number of subsets is not considered a fixed parameter, but is determined by the input (the number of sets is the number of integers divided by 3).
Greedy number partitioning – loops over the numbers, and puts each number in the set whose current sum is smallest. If the numbers are not sorted, then the runtime is O( n ) and the approximation ratio is at most 3/2 ("approximation ratio" means the larger sum in the algorithm output, divided by the larger sum in an optimal partition).
Splitting a column into multiple columns (e.g., converting a comma-separated list, specified as a string in one column, into individual values in different columns) Disaggregating repeating columns; Looking up and validating the relevant data from tables or referential files