- #1
Sebastien77
- 5
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Hi all,
I am looking for an efficient solution to solve the following problem. Can anybody help?
Assume a set S of elements ki and a set V of possible groupings Gj. A grouping Gj is a subset of S. Associate a weight wij to each mapping ki to Gj. The weights are infinite if ki ⊄ Gj, and finite signed number if ki ⊂ Gj.
1) Find the set of mappings from S to V minimizing the sum of the associated weights under the constraint that each element of S can be involved in exactly one or no mapping.
2) Same question but by changing the constraint to "under the constraint that each element of S must be involved in exactly one mapping".
Note: For my application V is a minute fraction of all possible groupings of the elements of S.Sébastien
I am looking for an efficient solution to solve the following problem. Can anybody help?
Assume a set S of elements ki and a set V of possible groupings Gj. A grouping Gj is a subset of S. Associate a weight wij to each mapping ki to Gj. The weights are infinite if ki ⊄ Gj, and finite signed number if ki ⊂ Gj.
1) Find the set of mappings from S to V minimizing the sum of the associated weights under the constraint that each element of S can be involved in exactly one or no mapping.
2) Same question but by changing the constraint to "under the constraint that each element of S must be involved in exactly one mapping".
Note: For my application V is a minute fraction of all possible groupings of the elements of S.Sébastien