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://www.soci.swt.edu/capps/prob.htm. http://mat.gsia.cmu.edu/GROUP95/0577.html. http://www.informs.org/Conf/WA96/TALKS/SB24.3.html. [Algorithms?] (1999-07-12) | ||||
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Assignment problem Definition from Language, Idioms & Slang Dictionaries & Glossaries
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assignment problem
assignment problem
(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.
assignment problem
(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.
Assignment problem Definition from Encyclopedia Dictionaries & Glossaries
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Assignment problem
The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. It consists of finding a maximum weight matching in a weighted bipartite graph.
In its most general form, the problem is as follows:
- There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one agent to each task in such a way that the total cost of the assignment is minimized.
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