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Packing circles in a square - closely related to spreading points in a unit square with the objective of finding the greatest minimal separation, d n, between points. To convert between these two formulations of the problem, the square side for unit circles will be L = 2 + 2 / d n {\displaystyle L=2+2/d_{n}} .
Does linear programming admit a strongly polynomial-time algorithm? (This is problem #9 in Smale's list of problems.) How many queries are required for envy-free cake-cutting? What is the algorithmic complexity of the minimum spanning tree problem? Equivalently, what is the decision tree complexity of the MST problem?
This problem has straightforward solutions in a sufficiently powerful OO programming system. Essentially, the circle–ellipse problem is one of synchronizing two representations of type: the de facto type based on the properties of the object, and the formal type associated with the object by the object system. If these two pieces of ...
There are 92 solutions. The problem was first posed in the mid-19th century. In the modern era, it is often used as an example problem for various computer programming techniques. The eight queens puzzle is a special case of the more general n queens problem of placing n non-attacking queens on an n×n chessboard.
Such lower bound is called a "separation bound" since it separates between the difference and 0. For example, if the absolute difference is at least 2-d, it means that we can round all numbers to d bits of accuracy, and solve SRS in time polynomial in d. This leads to the mathematical problem of proving bounds on this difference.
Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. [3]: ND25, ND27 Clique cover problem [2] [3]: GT17
For the example below, there are four sides: A, B, C and the final result ABC. A is a 10×30 matrix, B is a 30×5 matrix, C is a 5×60 matrix, and the final result is a 10×60 matrix. The regular polygon for this example is a 4-gon, i.e. a square: The matrix product AB is a 10x5 matrix and BC is a 30x60 matrix.
If, for example, there are two balls and three bins, then the number of ways of placing the balls is (+) = =. The table shows the six possible ways of distributing the two balls, the strings of stars and bars that represent them (with stars indicating balls and bars separating bins from one another), and the subsets that correspond to the strings.