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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 ...
A trivial example. In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountain climbers starting at sea level on the left and right sides of the mountain to meet at the summit, while maintaining equal altitudes at all times.
If the Erdős–Ulam problem has a positive solution, it would provide a counterexample to the Bombieri–Lang [4] [5] conjecture and to the abc conjecture. [6] It would also solve Harborth's conjecture, on the existence of drawings of planar graphs in which all distances are integers. If a dense rational-distance set exists, any straight-line ...
In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 [ 1 ] [ 2 ] and almost proven by Larry Guth and Nets Katz in 2015.
The jeep problem, [1] desert crossing problem [2] or exploration problem [3] is a mathematics problem in which a jeep must maximize the distance it can travel into a desert with a given quantity of fuel. The jeep can only carry a fixed and limited amount of fuel, but it can leave fuel and collect fuel at fuel dumps anywhere in the desert.
According to Hermann Weyl, the assumption that space is made of finite and discrete units is subject to a further problem, given by the "tile argument" or "distance function problem". [ 45 ] [ 46 ] According to this, the length of the hypotenuse of a right angled triangle in discretized space is always equal to the length of one of the two ...
Various algorithms exist that solve problems beside the computation of distance between a pair of strings, to solve related types of problems. Hirschberg's algorithm computes the optimal alignment of two strings, where optimality is defined as minimizing edit distance.
Edit distance matrix for two words using cost of substitution as 1 and cost of deletion or insertion as 0.5. For example, the Levenshtein distance between "kitten" and "sitting" is 3, since the following 3 edits change one into the other, and there is no way to do it with fewer than 3 edits: kitten → sitten (substitution of "s" for "k"),