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Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
The traveling tournament problem (TTP) is a mathematical optimization problem. The question involves scheduling a series of teams such that: Each team plays every other team twice, once at home and once in the other's stadium. No team plays the same opponent in two consecutive weeks.
[5] [6] The road shortens the trip by 43 km compared with the existing Route 13. The expressway toll will be 550 kip per kilometre, or about 62,000 kip for a one-way trip between Vientiane and Vang Vieng. [3] The trip from Vientiane to Vang Vieng is shortened from 4 hours to 1.5 hours using the expressway. [7]
In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process.
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems .
Upward planarity testing [8] Hospitals-and-residents problem with couples; Knot genus [38] Latin square completion (the problem of determining if a partially filled square can be completed) Maximum 2-satisfiability [3]: LO5 Maximum volume submatrix – Problem of selecting the best conditioned subset of a larger matrix
The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.
The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP ...
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