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The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
In combinatorics, stars and bars (also called "sticks and stones", [1] "balls and bars", [2] and "dots and dividers" [3]) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve a variety of counting problems, such as how many ways there are to put n indistinguishable balls into k distinguishable bins. [4]
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
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 ...
Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively. A point on a line gives a combination of 2p and 5p for its given total (green).
There are three forms of combination: (1) horizontal integration: the combination of firms in the same business lines and markets; (2) vertical integration: the combination of firms with operations in different but successive stages of production or distribution or both; (3) conglomeration: the combination of firms with unrelated and diverse ...
Texas Instruments BA II Plus Professional. The BA II Plus is the main financial calculator sold by Texas Instruments as of 2015. It provides basic scientific calculator functionality alongside its financial functions, and provides most of its financial functions in the form of worksheets, where values are input as variables in a table; when a computation is requested, the calculator plugs the ...
It is useful when both parties are willing to cooperate in implementing the fair solution. Such solutions, particularly the Nash solution, were used to solve concrete economic problems, such as management–labor conflicts, on numerous occasions. [1] An alternative approach to bargaining is the positive approach. It studies how the surplus is ...