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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
Many students work in groups to solve them and help get a better understanding of the material, [6] [7] but most professors require each student to hand in their own individual problem set. Some professors explicitly encourage collaboration, [ 5 ] [ 6 ] some allow it, and some explicitly disallow it [ 3 ] or consider it cheating.
Problem solving in psychology refers to the process of finding solutions to problems encountered in life. [5] Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping, in which the problem is discovered and simplified. The next step is to generate possible solutions and ...
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
A helpful discussion forum leading up to the problem release, a practice problem with live text chat discussion, can be found here. Below are previous problems: 2006 Problem – Solving the Social Security Stalemate 2007 Problem – Beat the Street! 2008 Problem – Energy Independence Meets the Law of Unintended Consequences
Modal analysis using FEM — solution of eigenvalue problems to find natural vibrations; Céa's lemma — solution in the finite-element space is an almost best approximation in that space of the true solution; Patch test (finite elements) — simple test for the quality of a finite element
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.