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This is a balanced assignment problem. Its solution is whichever combination of taxis and customers results in the least total cost. Now, suppose that there are four taxis available, but still only three customers. This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing ...
A Langford pairing for n = 4.. In combinatorial mathematics, a Langford pairing, also called a Langford sequence, is a permutation of the sequence of 2n numbers 1, 1, 2, 2, ..., n, n in which the two 1s are one unit apart, the two 2s are two units apart, and more generally the two copies of each number k are k units apart.
This problem can be seen as a generalization of the linear assignment problem. [2] In words, the problem can be described as follows: An instance of the problem has a number of agents (i.e., cardinality parameter) and a number of job characteristics (i.e., dimensionality parameter) such as task, machine, time interval, etc. For example, an ...
The addition of couples to the hospitals/residents problem renders the problem NP-complete. [16] The assignment problem seeks to find a matching in a weighted bipartite graph that has maximum weight. Maximum weighted matchings do not have to be stable, but in some applications a maximum weighted matching is better than a stable one.
In C and C++, the comma operator is similar to parallel assignment in allowing multiple assignments to occur within a single statement, writing a = 1, b = 2 instead of a, b = 1, 2. This is primarily used in for loops , and is replaced by parallel assignment in other languages such as Go. [ 20 ]
The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods.It was developed and published in 1955 by Harold Kuhn, who gave it the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry.
Flow Shop Scheduling Problem; Generalized assignment problem; Integer programming. The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling
Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem. In an assignment problem (also called house-allocation problem or one-sided matching), there are m objects and they have to be allocated among n agents, such that each agent receives at most one object. Examples include the assignment of ...