Assignment problem: Difference between revisions

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m Formal definition: Minor formatting fix
Fix formal definition removing a mistaken condition (requiring A and T to be of the same size together with contemplating unbalanced assignment is a contradiction).
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The formal definition of the '''assignment problem''' (or '''linear assignment problem''') is
 
:Given two sets, ''A'' and ''T'', of equal size, together with a [[weight function]] ''C'' : ''A'' × ''T'' → '''[[real number|R]]'''. Find a [[bijection]] ''f'' : ''A'' → ''T'' such that the [[Loss function|cost function]]:
::<math>\sum_{a\in A}C(a,f(a))</math>
:is minimized.