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English: Gray, blue, red, green, light green, black graph papers with 1 cm–0.5 cm–1 mm grids (page size: A4) in printable PDF format. Date 25 July 2013, 18:04:17
Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem [3]: SP13 Variations on the Traveling salesman problem. 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.
Hexagonal paper shows regular hexagons instead of squares. These can be used to map geometric tiled or tesselated designs among other uses. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.
In statistical quality control, the np-chart is a type of control chart used to monitor the number of nonconforming units in a sample.It is an adaptation of the p-chart and used in situations where personnel find it easier to interpret process performance in terms of concrete numbers of units rather than the somewhat more abstract proportion.
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 ...
As both n and L grow large, SSP is NP-hard. The complexity of the best known algorithms is exponential in the smaller of the two parameters n and L. The problem is NP-hard even when all input integers are positive (and the target-sum T is a part of the input). This can be proved by a direct reduction from 3SAT. [2]
This is the minimum number of crossings among all drawings of this graph, so the graph has crossing number cr(G) = 3. In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero. Determining the ...
In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI. Ladner's theorem , shown in 1975 by Richard E. Ladner , [ 1 ] is a result asserting that, if P ≠ NP , then NPI is not empty; that is, NP contains ...