About: Balanced number partitioning

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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 most k. Subject to this, it is required that the sums of sizes in the m subsets are as similar as possible.

Attributes	Values
rdfs:label	Balanced number partitioning (en)
rdfs:comment	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 most k. Subject to this, it is required that the sums of sizes in the m subsets are as similar as possible. (en)
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Clarify dbt:Reflist dbt:Rp
Subject	Number partitioning
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Balanced_number_partitioning?oldid=1068636367&ns=0
Wikipage page ID	69025670 (xsd:integer)
page length (characters) of wiki page	22644 (xsd:nonNegativeInteger)
Wikipage revision ID	1068636367 (xsd:integer)
Link from a Wikipage to another Wikipage	Flexible manufacturing system List scheduling Uniform matroid Very Large Scale Integration 3-partition problem Anytime algorithm Linear programming Optimal job scheduling Ordinal data Partition matroid Partition problem Identical-machines scheduling Absolutely integrable function Strong NP-completeness Longest-processing-time-first scheduling Largest differencing method Matroid-constrained number partitioning Maximum weight matching Multifit algorithm Multiway number partitioning Number partitioning
has abstract	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 most k. Subject to this, it is required that the sums of sizes in the m subsets are as similar as possible. An example application is identical-machines scheduling where each machine has a job-queue that can hold at most k jobs. The problem has applications also in manufacturing of VLSI chips, and in assigning tools to machines in flexible manufacturing systems. In the standard three-field notation for optimal job scheduling problems, the problem of minimizing the largest sum is sometimes deonted by "P \| # ≤ k \| Cmax". The middle field "# ≤ k" denotes that the number of jobs in each machine should be at most k. This is in contrast to the unconstrained version, which is denoted by "". (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Balanced_number_partitioning
is Wikipage redirect of	Balanced partition problem
is Link from a Wikipage to another Wikipage of	Longest-processing-time-first scheduling Largest differencing method Matroid-constrained number partitioning Multiway number partitioning Balanced partition problem
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Balanced_number_partitioning

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