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The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
The Break-Even Point can alternatively be computed as the point where Contribution equals Fixed Costs. The quantity, ( P − V ) {\displaystyle \left(P-V\right)} , is of interest in its own right, and is called the Unit Contribution Margin (C): it is the marginal profit per unit, or alternatively the portion of each sale that contributes to ...
"NP-complete problems are the most difficult known problems." Since NP-complete problems are in NP, their running time is at most exponential. However, some problems have been proven to require more time, for example Presburger arithmetic. Of some problems, it has even been proven that they can never be solved at all, for example the halting ...
In nuclear fusion research, the term break-even refers to a fusion energy gain factor equal to unity; this is also known as the Lawson criterion. The notion can also be found in more general phenomena, such as percolation. In energy, the break-even point is the point where usable energy gotten from a process equals the input energy.
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb, [ 4 ] Binh et al. [ 5 ] and Binh. [ 6 ] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which ...
For each combinatorial optimization problem, there is a corresponding decision problem that asks whether there is a feasible solution for some particular measure m 0. For example, if there is a graph G which contains vertices u and v, an optimization problem might be "find a path from u to v that uses the fewest edges". This problem might have ...
The cost breakdown analysis is even more effective when repeated constantly, so that changes in the respective shares in total costs of the various cost drivers can be tracked down. Over a five-year period, the share of expenses for tires might have risen from 5% to 8%, accompanied by a decrease of expenses for personnel from 35% to 32%, which ...