# assignment problem

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## assignment problem

[ə′sīn·mənt ′präb·ləm]
(computer science)
A special case of the transportation problem in a linear program, in which the number of sources (assignees) equals the number of designations (assignments) and each supply and each demand equals 1.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## assignment problem

(mathematics, algorithm)
(Or "linear assignment") Any problem involving minimising the sum of C(a, b) over a set P of pairs (a, b) where a is an element of some set A and b is an element of set B, and C is some function, under constraints such as "each element of A must appear exactly once in P" or similarly for B, or both.

For example, the a's could be workers and the b's projects.

The problem is "linear" because the "cost function" C() depends only on the particular pairing (a, b) and is independent of all other pairings.

http://forum.swarthmore.edu/epigone/comp.soft-sys.matlab/bringhyclu. http://soci.swt.edu/capps/prob.htm. http://mat.gsia.cmu.edu/GROUP95/0577.html. http://informs.org/Conf/WA96/TALKS/SB24.3.html.

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