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[1]: sec.5 The problem is parametrized by a positive integer k, and called k-way number partitioning. [2] The input to the problem is a multiset S of numbers (usually integers), whose sum is k*T. The associated decision problem is to decide whether S can be partitioned into k subsets such that the sum of each subset is exactly T.
The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. The main steps of the algorithm are: Order the numbers from large to small. Replace the largest and second-largest numbers by their difference. If two or more numbers remain, return to step 1.
Snowflake schema used by example query. The example schema shown to the right is a snowflaked version of the star schema example provided in the star schema article. The following example query is the snowflake schema equivalent of the star schema example code which returns the total number of television units sold by brand and by country for 1997.
In computer science, greedy number partitioning is a class of greedy algorithms for multiway number partitioning. The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers ...
Balanced number partitioning is a variant of multiway number partitioning in which there are constraints on the number of items allocated to each set. The input to the problem is a set of n items of different sizes, and two integers m, k. The output is a partition of the items into m subsets, such that the number of items in each subset is at ...
Consider the example of [5, 2, 3, 1, 0], following the scheme, after the first partition the array becomes [0, 2, 1, 3, 5], the "index" returned is 2, which is the number 1, when the real pivot, the one we chose to start the partition with was the number 3. With this example, we see how it is necessary to include the returned index of the ...
Equal-cardinality partition is a variant in which both parts should have an equal number of items, in addition to having an equal sum. This variant is NP-hard too. [5]: SP12 Proof. Given a standard Partition instance with some n numbers, construct an Equal-Cardinality-Partition instance by adding n zeros. Clearly, the new instance has an equal ...
In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by (,) or {}. [1]