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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 key to solving a problem recursively is to recognize that it can be broken down into a collection of smaller sub-problems, to each of which that same general solving procedure that we are seeking applies [citation needed], and the total solution is then found in some simple way from those sub-problems' solutions. Each of these created sub ...
Closer to the Collatz problem is the following universally quantified problem: Given g, does the sequence of iterates g k (n) reach 1, for all n > 0? Modifying the condition in this way can make a problem either harder or easier to solve (intuitively, it is harder to justify a positive answer but might be easier to justify a negative one).
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields.
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 ...
In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m 0, m 1, m 2, ...), does there exist a positive Borel measure μ (for instance, the measure determined by the cumulative distribution function of a random variable) on the real line such that
General Problem Solver (GPS) is a computer program created in 1957 by Herbert A. Simon, J. C. Shaw, and Allen Newell (RAND Corporation) intended to work as a universal problem solver machine. In contrast to the former Logic Theorist project, the GPS works with means–ends analysis .
The sequence can be used to prove that there are infinitely many prime numbers, as any prime can divide at most one number in the sequence. More strongly, no prime factor of a number in the sequence can be congruent to 5 modulo 6, and the sequence can be used to prove that there are infinitely many primes congruent to 7 modulo 12. [20]